Deck 7: Conic Sections

Question 1

Graph Ellipses Not Centered at the Origin
$$\frac { ( x + 1 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

A)

B)

C)

D)

Answer 1

A

Question 2

Write Equations of Ellipses in Standard Form

Center at $( - 1,1 )$

A) $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y - 1 ) ^ { 2 } } { 9 } = 1$
foci at $( - 1 + 3 \sqrt { 3 } , 1 )$ and $( - 1 - 3 \sqrt { 3 } , 1 )$
B) $\frac { ( x + 1 ) ^ { 2 } } { 9 } + \frac { ( y - 1 ) ^ { 2 } } { 36 } = 1$
foci at $( 1 + 3 \sqrt { 3 } , - 1 )$ and $( 1 - 3 \sqrt { 3 } , - 1 )$
C) $\frac { ( x - 1 ) ^ { 2 } } { 9 } + \frac { ( y + 1 ) ^ { 2 } } { 36 } = 1$
foci at $( - 3 \sqrt { 3 } , 1 )$ and $( 3 \sqrt { 3 } , 1 )$
D) $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$
foci at $( - 1 + 3 \sqrt { 3 } , - 1 )$ and $( - 1 - 3 \sqrt { 3 } , - 1 )$

Answer 2

A

Question 3

Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis vertical with length 14; length of minor axis = 6; center (0, 0) A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 49 } = 1$
B) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 49 } = 1$
D) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 196 } = 1$

Answer 3

A

Question 4

Graph the ellipse and locate the foci.
$$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 40 } = 1$$

A) foci at $( 3,0 )$ and $( - 3,0 )$

B) foci at $( 0,7 )$ and $( 0 , - 7 )$

C) foci at $( 2 \sqrt { 10 } , 0 )$ and $( - 2 \sqrt { 10 } , 0 )$

D) foci at $( 0,3 )$ and $( 0 , - 3 )$

Question 5

Graph Ellipses Not Centered at the Origin
$$\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$$

A)

B)

C)

D)

Question 6

Graph the ellipse and locate the foci.
$$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$$

A) foci at $( 0 , \sqrt { 39 } )$ and $( 0 , - \sqrt { 39 } )$

B) foci at $( \sqrt { 39 } , 0 )$ and $( - \sqrt { 39 } , 0 )$

C) foci at $( 2 \sqrt { 14 } , 0 )$ and $( - 2 \sqrt { 14 } , 0 )$

D) foci at $( 0,2 \sqrt { 14 } )$ and $( 0 , - 2 \sqrt { 14 } )$

Question 7

Find the standard form of the equation of the ellipse satisfying the given conditions.
Major axis horizontal with length 20; length of minor axis = 16; center (0, 0) A) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1$
B) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 100 } = 1$
C) $\frac { x ^ { 2 } } { 20 } + \frac { y ^ { 2 } } { 64 } = 1$
D) $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 256 } = 1$

Question 8

Write Equations of Ellipses in Standard Form

A) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$
foci at $( 0 , - \sqrt { 13 } )$ and $( 0 , \sqrt { 13 } )$
B) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 36 } = 1$

foci at $( 0 , - \sqrt { 13 } )$ and $( 0 , \sqrt { 13 } )$
C) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$
foci at $( 0 , - 7 )$ and $( 0,7 )$
D) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$

foci at $( 0,7 )$ and $( 6,0 )$

Question 9

Graph the ellipse and locate the foci.
$$4 x ^ { 2 } = 36 - 9 y ^ { 2 }$$

A) foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$

B) foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$

C) foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$

D) foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

Question 10

Graph the ellipse and locate the foci.
$$\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$$

A) foci at $( 0,5 )$ and $( 0 , - 5 )$

B) foci at $( 5,0 )$ and $( - 5,0 )$

C) foci at $( 0,2 \sqrt { 6 } )$ and $( 0 , - 2 \sqrt { 6 } )$

D) foci at $( 0,7 )$ and $( 0 , - 7 )$

Question 11

Find the standard form of the equation of the ellipse satisfying the given conditions.
Foci: $( 0 , - 4 ) , ( 0,4 )$ ; vertices: $( 0 , - 7 ) , ( 0,7 )$

A) $\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = 1$
B) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$
C) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 33 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$

Question 12

Graph the ellipse and locate the foci.
$$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$$

A)
foci at $( 2 \sqrt { 14 } , 0 )$ and $( - 2 \sqrt { 14 } , 0 )$

B) foci at $( 0,2 \sqrt { 14 } )$ and $( 0 , - 2 \sqrt { 14 } )$

C) foci at $( 5 \sqrt { 3 } , 0 )$ and $( - 5 \sqrt { 3 } , 0 )$

D) foci at $( 0,5 \sqrt { 3 } )$ and $( 0 , - 5 \sqrt { 3 } )$

Question 13

Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: (2, -8)and (2, 0); endpoints of minor axis: (0, -4)and (4, -4); A) $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 4 ) ^ { 2 } } { 16 } = 1$
B) $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$
C) $\frac { ( x + 2 ) ^ { 2 } } { 4 } + \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$
D) $\frac { ( x + 4 ) ^ { 2 } } { 4 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$

Question 14

Write Equations of Ellipses in Standard Form

A) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 9 } = 1$
foci at $( - 2 \sqrt { 10 } , 0 )$ and $( 2 \sqrt { 10 } , 0 )$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 49 } = 1$
foci at $( - 2 \sqrt { 10 } , 0 )$ and $( 2 \sqrt { 10 } , 0 )$
C) $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 9 } = 1$
foci at $( - 2 \sqrt { 10 } , 0 )$ and $( 2 \sqrt { 10 } , 0 )$
D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 9 } = 1$
foci at $( - 7,0 )$ and $( 7,0 )$

Question 15

Graph Ellipses Not Centered at the Origin
$$4 ( x - 1 ) ^ { 2 } + 16 ( y - 2 ) ^ { 2 } = 64$$

A)

B)

C)

D)

Question 16

Graph the ellipse and locate the foci.
$$9 x ^ { 2 } + 4 y ^ { 2 } = 36$$

A) foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$

B) foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$

C) foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$

D) foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

Question 17

Find the standard form of the equation of the ellipse satisfying the given conditions.
Foci: $( 0 , - 2 ) , ( 0,2 ) ; y$ -intercepts: $- 5$ and 5

A) $\frac { x ^ { 2 } } { 21 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 21 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 21 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$

Question 18

Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: (-10, -4)and (6, -4); endpoints of minor axis: (-2, -8)and (-2, 0) A) $\frac { ( x + 2 ) ^ { 2 } } { 64 } + \frac { ( y + 4 ) ^ { 2 } } { 16 } = 1$
B) $\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 64 } = 1$
C) $\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { ( y - 4 ) ^ { 2 } } { 16 } = 0$
D) $\frac { ( x - 2 ) ^ { 2 } } { 64 } + \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$

Question 19

Find the standard form of the equation of the ellipse satisfying the given conditions.
Foci: $( - 2,0 ) , ( 2,0 ) ; x$ -intercepts: $- 5$ and 5

A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 21 } = 1$
B) $\frac { x ^ { 2 } } { 21 } + \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 21 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1$

Question 20

Find the standard form of the equation of the ellipse satisfying the given conditions.
Foci: $( - 3,0 ) , ( 3,0 )$ ; vertices: $( - 4,0 ) , ( 4,0 )$

A) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1$
B) $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 7 } = 1$
D) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 21

Find the foci of the ellipse whose equation is given.
$$25 ( x + 3 ) ^ { 2 } + 36 ( y + 1 ) ^ { 2 } = 900$$

A) foci at $( - 3 + \sqrt { 11 } , - 1 )$ and $( - 3 - \sqrt { 11 } , - 1 )$
B) foci at $( - 1 + \sqrt { 11 } , - 3 )$ and $( - 1 - \sqrt { 11 } , - 3 )$
C) foci at $( - \sqrt { 11 } , - 1 )$ and $( \sqrt { 11 } , - 1 )$
D) foci at $( - 3 + \sqrt { 11 } , - 3 )$ and $( - 3 - \sqrt { 11 } , - 3 )$

Question 22

Find the vertices and locate the foci for the hyperbola whose equation is given.
$\frac { \mathrm { x } ^ { 2 } } { 144 } - \frac { \mathrm { y } ^ { 2 } } { 4 } = 1$

A) vertices: $( - 12,0 ) , ( 12,0 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$
B) vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$
C) vertices: $( 0 , - 12 ) , ( 0,12 )$
foci: $( - 2 \sqrt { 37 } , 0 ) , ( 2 \sqrt { 37 } , 0 )$
D) vertices: $( - 12,0 ) , ( 12,0 )$
foci: $( - 2,0 ) , ( 2,0 )$

Question 23

Solve Applied Problems Involving Ellipses
Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and the height of the arch over the center of the roadway is 11 feet. Two trucks plan to
Use this road. They are both 8 feet wide. Truck 1 has an overall height of 10 feet and Truck 2 has an overall
Height of 9 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the
Bridge.

A)Both Truck 1 and Truck 2 can pass under the bridge.
B)Neither Truck 1 nor Truck 2 can pass under the bridge.
C)Truck 1 can pass under the bridge, but Truck 2 cannot.
D)Truck 2 can pass under the bridge, but Truck 1 cannot.

Question 24

Solve Applied Problems Involving Ellipses
Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 30 feet and the height of the arch over the center of the roadway is 13 feet. Two trucks plan to
Use this road. They are both 10 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an
Overall height of 13 feet. Draw a rough sketch of the situation and determine which of the trucks can pass
Under the bridge.

A)Truck 1 can pass under the bridge, but Truck 2 cannot.
B)Both Truck 1 and Truck 2 can pass under the bridge.
C)Neither Truck 1 nor Truck 2 can pass under the bridge.
D)Truck 2 can pass under the bridge, but Truck 1 cannot.

Question 25

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
$$\left\{ \begin{array} { l } \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1 \\y = 3\end{array} \right.$$

A) $\{ ( 0,3 ) \}$
B) $\{ ( 3,3 ) \}$
C) $\{ ( 3,0 ) \}$
D) $\{ ( 0,3 ) , ( 0 , - 3 ) \}$

Question 26

Find the foci of the ellipse whose equation is given.
$$\frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { ( y + 2 ) ^ { 2 } } { 36 } = 1$$

A) foci at $( 3 , - 2 - \sqrt { 11 } )$ and $( 3 , - 2 + \sqrt { 11 } )$
B) foci at $( - 2,3 - \sqrt { 11 } )$ and $( - 2,3 + \sqrt { 11 } )$
C) foci at $( - 3 , - 2 - \sqrt { 11 } )$ and $( - 3 , - 2 + \sqrt { 11 } )$
D) foci at $( 4 , - 2 - \sqrt { 11 } )$ and $( 4 , - 2 + \sqrt { 11 } )$

Question 27

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
$$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = 7\end{array} \right.$$

A) $\{ ( 4,3 ) , ( 3,4 ) \}$
B) $\{ ( - 4,3 ) , ( - 3,4 ) \}$
C) $\{ ( 4 , - 3 ) , ( 3 , - 4 ) \}$
D) $\{ ( - 4 , - 3 ) , ( - 3 , - 4 ) \}$

Question 28

Find the vertices and locate the foci for the hyperbola whose equation is given.
$$y = \pm \sqrt { x ^ { 2 } - 6 }$$

A) vertices: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$
B) vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - \sqrt { 6 } , 0 ) , ( \sqrt { 6 } , 0 )$
C) vertices: $( - 6,0 ) , ( 6,0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$
D) vertices: $( 0 , - \sqrt { 6 } ) , ( 0 , \sqrt { 6 } )$
foci: $( 0 , - 2 \sqrt { 3 } ) , ( 0,2 \sqrt { 3 } )$

Question 29

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
$$\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\25 x ^ { 2 } + 16 y ^ { 2 } = 400\end{array} \right.$$

A) $\{ ( 0,5 ) , ( 0 , - 5 ) \}$
B) $\{ ( 5,0 ) , ( - 5,0 ) \}$
C) $\{ ( 0,4 ) , ( 0 , - 4 ) \}$
D) $\{ ( 4,0 ) , ( - 4,0 ) \}$

Question 30

Convert the equation to the standard form for an ellipse by completing the square on x and y.
$$25 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 0$$

A) $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x - 2 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$
D) $\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1$

Question 31

Graph the semi-ellipse.
$$y = - \sqrt { 16 - 9 x ^ { 2 } }$$

A)

B)

C)

D)

Question 32

Find the vertices and locate the foci for the hyperbola whose equation is given.
$$\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 121 } = 1$$

A) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( 0 , - \sqrt { 221 } ) , ( 0 , \sqrt { 221 } )$
B) vertices: $( - 11,0 ) , ( 11,0 )$
foci: $( - \sqrt { 221 } , 0 ) , ( \sqrt { 221 } , 0 )$
C) vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( - \sqrt { 221 } , 0 ) , ( \sqrt { 221 } , 0 )$
D) vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 11,0 ) , ( 11,0 )$

Question 33

Graph Ellipses Not Centered at the Origin
$$16 ( x - 1 ) ^ { 2 } + 4 ( y - 2 ) ^ { 2 } = 64$$

A)

B)

C)

D)

Question 34

Solve Applied Problems Involving Ellipses
Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 30 feet and the height of the arch over the center of the roadway is 13 feet. Two trucks plan to
Use this road. They are both 12 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an
Overall height of 11 feet. Draw a rough sketch of the situation and determine which of the trucks can pass
Under the bridge.

A)Truck 2 can pass under the bridge, but Truck 1 cannot.
B)Both Truck 1 and Truck 2 can pass under the bridge.
C)Neither Truck 1 nor Truck 2 can pass under the bridge.
D)Truck 1 can pass under the bridge, but Truck 2 cannot.

Question 35

Find the foci of the ellipse whose equation is given.
$$\frac { ( x - 3 ) ^ { 2 } } { 36 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

A) foci at $( 3 + 2 \sqrt { 5 } , 1 )$ and $( 3 - 2 \sqrt { 5 } , 1 )$
B) foci at $( 1 + 2 \sqrt { 5 } , 3 )$ and $( 1 - 2 \sqrt { 5 } , 3 )$
C) foci at $( - 2 \sqrt { 5 } , 1 )$ and $( 2 \sqrt { 5 } , 1 )$
D) foci at $( 3 + 2 \sqrt { 5 } , 3 )$ and $( 3 - 2 \sqrt { 5 } , 3 )$

Question 36

Find the foci of the ellipse whose equation is given.
$$36 ( \mathrm { x } - 1 ) ^ { 2 } + 25 ( \mathrm { y } - 3 ) ^ { 2 } = 900$$

A) foci at $( 1,3 - \sqrt { 11 } )$ and $( 1,3 + \sqrt { 11 } )$
B) foci at $( 3,1 - \sqrt { 11 } )$ and $( 3,1 + \sqrt { 11 } )$
C) foci at $( - 1,3 - \sqrt { 11 } )$ and $( - 1,3 + \sqrt { 11 } )$
D) foci at $( 2,3 - \sqrt { 11 } )$ and $( 2,3 + \sqrt { 11 } )$

Question 37

Convert the equation to the standard form for an ellipse by completing the square on x and y.
$$25 x ^ { 2 } + 36 y ^ { 2 } - 50 x - 216 y - 551 = 0$$

A) $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 3 ) ^ { 2 } } { 36 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$
D) $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$

Question 38

Find the vertices and locate the foci for the hyperbola whose equation is given.
$$16 x ^ { 2 } - 4 y ^ { 2 } = 64$$

A) vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$
B) vertices: $( 0 , - 2 ) , ( 0,2 )$
foci: $( 0 , - 2 \sqrt { 5 } ) , ( 0,2 \sqrt { 5 } )$
C) vertices: $( - 2,0 ) , ( 2,0 )$
foci: $( - 2 \sqrt { 3 } , 0 ) , ( 2 \sqrt { 3 } , 0 )$
D) vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 2 \sqrt { 5 } , 0 ) , ( 2 \sqrt { 5 } , 0 )$

Question 39

Write Equations of Hyperbolas in Standard Form
Foci: (-5, 0), (5, 0); vertices: (-2, 0), (2, 0) A) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 21 } = 1$
B) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 21 } = 1$
C) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$

Question 40

Find the vertices and locate the foci for the hyperbola whose equation is given.
$25 \mathrm { y } ^ { 2 } - 9 \mathrm { x } ^ { 2 } = 225$

A) vertices: $( 0 , - 3 ) , ( 0,3 )$
foci: $( 0 , - \sqrt { 34 } ) , ( 0 , \sqrt { 34 } )$
B) vertices: $( - 3,0 ) , ( 3,0 )$
foci: $( - \sqrt { 34 } , 0 ) , ( \sqrt { 34 } , 0 )$
C) vertices: $( - 5,0 ) , ( 5,0 )$
foci: $( - 4,0 ) , ( 4,0 )$
D) vertices: $( 0 , - 5 ) , ( 0,5 )$
foci: $( 0 , - \sqrt { 34 } ) , ( 0 , \sqrt { 34 } )$

Question 41

Graph Hyperbolas Centered at the Origin
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
$$\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$$

A) Asymptotes: $y = \pm \frac { 3 } { 5 } x$

B) Asymptotes: $y = \pm \frac { 5 } { 3 } x$

C) Asymptotes: $\mathrm { y } = \pm \frac { 3 } { 5 } \mathrm { x }$

D) Asymptotes: $y = \pm \frac { 5 } { 3 } x$

Question 42

Find the standard form of the equation of the hyperbola.

A) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$
B) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$

Question 43

Graph Hyperbolas Not Centered at the Origin
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
$$( x + 4 ) ^ { 2 } - 4 ( y - 4 ) ^ { 2 } = 4$$

A) Center: $( - 4,4 )$ ; Vertices: $( - 6,4 )$ and $( - 2,4 )$ ; Foci: $( - 4 - \sqrt { 5 } , 4 )$ and $( - 4 + \sqrt { 5 } , 4 )$
B) Center: $( 4 , - 4 )$ ; Vertices: $( 2 , - 4 )$ and $( 6 , - 4 )$ ; Foci: $( 4 - \sqrt { 5 } , 4 )$ and $( 4 + \sqrt { 5 } , 4 )$
C) Center: $( - 4,4 )$ ; Vertices: $( - 5,5 )$ and $( - 1,5 )$ ; Foci: $( - 3 - \sqrt { 5 } , 5 )$ and $( - 3 + \sqrt { 5 } , 5 )$
D) Center: $( - 4,4 )$ ; Vertices: $( 2,4 )$ and $( - 2,4 )$ ; Foci: $( - \sqrt { 5 } , 4 )$ and $( \sqrt { 5 } , 4 )$

Question 44

Graph Hyperbolas Centered at the Origin
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
$$36 y ^ { 2 } - 4 x ^ { 2 } = 144$$

A) Asymptotes: $y = \pm \frac { 1 } { 3 } x$

B) Asymptotes: $\mathrm { y } = \pm 3 \mathrm { x }$

C) Asymptotes: $\mathrm { y } = \pm \frac { 1 } { 3 } \mathrm { x }$

D) Asymptotes: $\mathrm { y } = \pm 3 \mathrm { x }$

Question 45

Graph Hyperbolas Centered at the Origin
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
$4 x^{2}-9 y^{2}=36$

A) Asymptotes: $y = \pm \frac { 2 } { 3 } x$

B) Asymptotes: $y = \pm \frac { 3 } { 2 } x$

C) Asymptotes: $y = \pm \frac { 3 } { 2 } x$

D) Asymptotes: $y = \pm \frac { 2 } { 3 } x$

Question 46

Find the standard form of the equation of the hyperbola.

A) $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$
B) $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$
D) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 4 } = 1$

Question 47

Write Equations of Hyperbolas in Standard Form
Endpoints of transverse axis: $( 0 , - 6 ) , ( 0,6 )$ ; asymptote: $\mathrm { y } = \frac { 3 } { 10 } \mathrm { x }$

A) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 400 } = 1$
B) $\frac { y ^ { 2 } } { 400 } - \frac { x ^ { 2 } } { 36 } = 1$
C) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$
D) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$

Question 48

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
$$4 y ^ { 2 } - 25 x ^ { 2 } - 16 y - 100 x - 184 = 0$$

A) $\frac { ( y - 2 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 4 } = 1$
В) $\frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( y - 2 ) ^ { 2 } } { 4 } - \frac { ( x + 2 ) ^ { 2 } } { 25 } = 1$
D) $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$

Question 49

Write Equations of Hyperbolas in Standard Form
Endpoints of transverse axis: $( - 4,0 ) , ( 4,0 )$ ; foci: $( - 9,0 ) , ( - 9,0 )$

A) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 65 } = 1$
B) $\frac { x ^ { 2 } } { 65 } - \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 81 } = 1$
D) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 16 } = 1$

Question 50

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
$$4 x ^ { 2 } - 16 y ^ { 2 } - 16 x - 32 y - 64 = 0$$

A) $\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$
B) $\frac { ( x + 2 ) ^ { 2 } } { 16 } - \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( x - 2 ) ^ { 2 } } { 16 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
D) $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$

Question 51

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
$$x ^ { 2 } - y ^ { 2 } - 4 x + 4 y - 1 = 0$$

A) $( x - 2 ) ^ { 2 } - ( y - 2 ) ^ { 2 } = 1$
B) $( y - 2 ) ^ { 2 } - ( x - 2 ) ^ { 2 } = 1$
C) $( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 1$
D) $\frac { ( y - 2 ) ^ { 2 } } { 16 } - \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$

Question 52

Graph Hyperbolas Not Centered at the Origin
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
$$\frac { ( y - 1 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 100 } = 1$$

A) Center: $( 2,1 )$ ; Vertices: $( 2 , - 2 )$ and $( 2,4 )$ ; Foci: $( 2,1 - \sqrt { 109 } )$ and $( 2,1 + \sqrt { 109 } )$
B) Center: $( - 2 , - 1 )$ ; Vertices: $( - 2 , - 4 )$ and $( - 2,2 )$ ; Foci: $( - 2 , - 1 - \sqrt { 109 } )$ and $( - 2 , - 1 + \sqrt { 109 } )$
C) Center: $( 2,1 )$ ; Vertices: $( 2,1 - \sqrt { 109 } )$ and $( 2,1 + \sqrt { 109 } )$ ; Foci: $( 2 , - 2 )$ and $( 2,4 )$
D) Center: $( 2,1 )$ ; Vertices: $( 2 , - 1 )$ and $( 3,5 )$ ; Foci: $( 2,2 - \sqrt { 109 } )$ and $( 3,2 + \sqrt { 109 } )$

Question 53

Graph Hyperbolas Not Centered at the Origin
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
$$\frac { ( x - 1 ) ^ { 2 } } { 49 } - \frac { ( y + 4 ) ^ { 2 } } { 36 } = 1$$

A) Center: $( 1 , - 4 )$ ; Vertices: $( - 6 , - 4 )$ and $( 8 , - 4 )$ ; Foci: $( 1 - \sqrt { 85 } , - 4 )$ and $( 1 + \sqrt { 85 } , - 4 )$
B) Center: $( - 1,4 )$ ; Vertices: $( - 8,4 )$ and $( 6,4 )$ ; Foci: $( - 1 - \sqrt { 85 } , 4 )$ and $( - 1 + \sqrt { 85 } , 4 )$
C) Center: $( 1 , - 4 )$ ; Vertices: $( - 6,4 )$ and $( 8,4 )$ ; Foci: $( 1 - \sqrt { 85 } , 4 )$ and $( 1 + \sqrt { 85 } , 4 )$
D) Center: $( 1 , - 4 )$ ; Vertices: $( - 5 , - 4 )$ and $( 9 , - 4 )$ ; Foci: $( 2 + \sqrt { 85 } , - 3 )$ and $( - 3 + \sqrt { 85 } , - 3 )$

Question 54

Graph Hyperbolas Centered at the Origin
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
$$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$$

A) Asymptotes: $y = \pm 2 x$

B) Asymptotes: $y = \pm \frac { 1 } { 2 } x$

C) Asymptotes: $y = \pm 2 x$

D) Asymptotes: $y = \pm \frac { 1 } { 2 } x$

Question 55

Write Equations of Hyperbolas in Standard Form
Center: $( 6,3 ) ;$ Focus: $( 4,3 ) ;$ Vertex: $( 5,3 )$

A) $( x - 6 ) ^ { 2 } - \frac { ( y - 3 ) ^ { 2 } } { 3 } = 1$
B) $\frac { ( x - 6 ) ^ { 2 } } { 3 } - ( y - 3 ) ^ { 2 } = 1$
C) $( x - 3 ) ^ { 2 } - \frac { ( y - 6 ) ^ { 2 } } { 3 } = 1$
D) $\frac { ( x - 3 ) ^ { 2 } } { 3 } - ( y - 6 ) ^ { 2 } = 1$

Question 56

Find the standard form of the equation of the hyperbola.

A) $\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x - 2 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( y - 1 ) ^ { 2 } } { 25 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( x - 2 ) ^ { 2 } } { 25 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
D) $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$

Question 57

Graph Hyperbolas Centered at the Origin
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
$$y = \pm \sqrt { x ^ { 2 } - 6 }$$

A) Asymptotes: $y = \pm x$

B) Asymptotes: $y = \pm 3 x$

C) Asymptotes: $y = \pm \frac { 1 } { 3 } x$

D) Asymptotes: $y = \pm x$

Question 58

Write Equations of Hyperbolas in Standard Form
Foci: (0, -5), (0, 5); vertices: (0, -3), (0, 3) A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$
B) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$

Question 59

Graph Hyperbolas Not Centered at the Origin
Find the location of the center, vertices, and foci for the hyperbola described by the equation.
$$( y - 1 ) ^ { 2 } - 4 ( x - 3 ) ^ { 2 } = 4$$

A) Center: $( 3,1 )$ ; Vertices: $( 3 , - 1 )$ and $( 3,3 )$ ; Foci: $( 3,1 - \sqrt { 5 } )$ and $( 3,1 + \sqrt { 5 } )$
B) Center: $( - 3 , - 1 )$ ; Vertices: $( - 3 , - 3 )$ and $( - 3,1 )$ ; Foci: $( - 3 , - 1 - \sqrt { 5 } )$ and $( - 3 , - 1 + \sqrt { 5 } )$
C) Center: $( 3,1 )$ ; Vertices: $( - 3 , - 2 )$ and $( 3,2 ) ;$ Foci: $( 3 , - \sqrt { 5 } )$ and $( 3 , \sqrt { 5 } )$
D) Center: $( 3,1 )$ ; Vertices: $( 4,0 )$ and $( 4,4 )$ ; Foci: $( 4,2 - \sqrt { 5 } )$ and $( 4,2 + \sqrt { 5 } )$

Question 60

Convert the equation to the standard form for a hyperbola by completing the square on x and y.
$$\mathrm { y } ^ { 2 } - 16 \mathrm { x } ^ { 2 } - 4 \mathrm { y } + 64 \mathrm { x } - 76 = 0$$

A) $\frac { ( y - 2 ) ^ { 2 } } { 16 } - ( x - 2 ) ^ { 2 } = 1$
B) $\frac { ( x - 2 ) ^ { 2 } } { 16 } - ( y - 2 ) ^ { 2 } = 1$
C) $\frac { ( y - 4 ) ^ { 2 } } { 16 } - ( x - 4 ) ^ { 2 } = 1$
D) $( x - 2 ) ^ { 2 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$

Question 61

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
$$x ^ { 2 } = - 8 y$$

A)

B)

C)

D)

Question 62

Solve Applied Problems Involving Hyperbolas
Solve the problem.
Two recording devices are set 2600 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?

A) $977.78$ feet
B) $2900.86$ feet
C) $1236.93$ feet
D) $1648.04$ feet

Question 63

Use the center, vertices, and asymptotes to graph the hyperbola.
$$( x + 2 ) ^ { 2 } - 4 ( y + 2 ) ^ { 2 } = 4$$

A)

B)

C)

D)

Question 64

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
$$y ^ { 2 } = - 12 x$$

A) focus: $( - 3,0 )$
directrix: $x = 3$
B) focus: $( 0 , - 3 )$
directrix: $y = 3$
C) focus: $( 3,0 )$
directrix: $x = - 3$
D) focus: $( - 3,0 )$
directrix: $y = 3$

Question 65

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
$$x ^ { 2 } = 40 y$$

A) focus: $( 0,10 )$
directrix: $y = - 10$
B) focus: $( 10,0 )$
directrix: $y = 10$
C) focus: $( 10,0 )$
directrix: $x = 10$
D) focus: $( 0 , - 10 )$
directrix: $\mathrm { x } = - 10$

Question 66

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
$$\begin{array} { l } x ^ { 2 } - y ^ { 2 } = 9 \\x ^ { 2 } + y ^ { 2 } = 9\end{array}$$

A) $\{ ( 3,0 ) , ( - 3,0 ) \}$
B) $\{ ( 0,3 ) , ( 0 , - 3 ) \}$
C) $\{ ( 3,0 ) \}$
D) $\{ ( 0,3 ) \}$

Question 67

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
$$x ^ { 2 } = - 16 y$$

A) focus: $( 0 , - 4 )$
directrix: $y = 4$
B) focus: $( - 8,0 )$
directrix: $x = 4$
C) focus: $( 0 , - 4 )$
directrix: $y = - 4$
D) focus: $( 0,4 )$
directrix: $y = - 4$

Question 68

Use the center, vertices, and asymptotes to graph the hyperbola.
$$\frac { ( x + 1 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

A)

B)

C)

D)
11ecbe12_bedf_f697_88d3_9faa96c6c770_TB1195_11

Question 69

Solve Applied Problems Involving Hyperbolas
Solve the problem.
Two LORAN stations are positioned 278 miles apart along a straight shore. A ship records a time difference of 0.00086 seconds between the LORAN signals. (The radio signals travel at 186,000 miles per
Second.)Where will the ship reach shore if it were to follow the hyperbola corresponding to this time
Difference? If the ship is 200 miles offshore, what is the position of the ship?

A)59 miles from the master station, (161.9, 200)
B)80 miles from the master station, (200, 161.9)
C)59 miles from the master station, (200, 161.9)
D)80 miles from the master station, (161.9, 200)

Question 70

Additional Concepts
Use the relation's graph to determine its domain and range.
$$\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1$$

A) Domain: $[ - 4,4 ]$
Range: $[ - 2,2 ]$
B) Domain: $[ - 2,2 ]$
Range: $[ - 4,4 ]$
C) Domain: $( - 4,4 )$
Range: $( - 2,2 )$
D) Domain: $[ - 4,4 ]$
$\text { Range: }(-\infty, \infty)$

Question 71

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
$$x = 6 y ^ { 2 }$$

A) focus: $\left( \frac { 1 } { 24 } , 0 \right)$
directrix: $x = - \frac { 1 } { 24 }$
B) focus: $\left( 0 , \frac { 1 } { 24 } \right)$
directrix: $\mathrm { y } = - \frac { 1 } { 24 }$
C) focus: $\left( \frac { 1 } { 6 } , 0 \right)$
directrix: $x = - \frac { 1 } { 6 }$
D) focus: $\left( \frac { 1 } { 24 } , 0 \right)$
directrix: $x = \frac { 1 } { 24 }$

Question 72

Use the center, vertices, and asymptotes to graph the hyperbola.
$$( y - 2 ) ^ { 2 } - ( x - 1 ) ^ { 2 } = 3$$

A)

B)

C)

D)

Question 73

Use the center, vertices, and asymptotes to graph the hyperbola.
$(y+4)^{2}-4(x+3)^{2}=4$

A)

B)

C)

D)

Question 74

Additional Concepts
Use the relation's graph to determine its domain and range.
$$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$$

A) Domain: $( - \infty , - 2 ]$ or $[ 2 , \infty )$
Range: $( - \infty , \infty )$
B) Domain: $( - \infty , \infty )$
Range: $( - \infty , - 2 )$ or $( 2 , \infty )$
C) Domain: $( - \infty , - 2 ]$ and $[ 2 , \infty )$
Range: $( - \infty , \infty )$
D) Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$

Question 75

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate
system and finding points of intersection.
$$\begin{aligned}16 x ^ { 2 } + y ^ { 2 } & = 16 \\y ^ { 2 } - 16 x ^ { 2 } & = 16\end{aligned}$$

A) $\{ ( 0 , - 4 ) , ( 0,4 ) \}$
B) $\{ ( 0 , - 4 ) \}$
C) $\{ ( 0,16 ) \}$
D) $\{ ( 4,0 ) , ( 4,0 ) \}$

Question 76

Use the center, vertices, and asymptotes to graph the hyperbola.
$$\frac { ( y + 2 ) ^ { 2 } } { 9 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$$

A)

B)

C)

D)

Question 77

Solve Applied Problems Involving Hyperbolas
Solve the problem.
A satellite following the hyperbolic path shown in the picture turns rapidly at $( 0,3 )$ and then moves closer and closer to the line $\mathrm { y } = \frac { 5 } { 2 } \mathrm { x }$ as it gets farther from the tracking station at the origin. Find the equation that describes the path of the satellite if the center of the hyperbola is at $( 0,0 )$ .

A) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { \frac { 36 } { 25 } } = 1$
B) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { \left( \frac { 75 } { 6 } \right) ^ { 2 } } = 1$
C) $\frac { y ^ { 2 } } { \frac { 36 } { 25 } } - \frac { x ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { \left( \frac { 75 } { 6 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 9 } = 1$

Question 78

Additional Concepts
Use the relation's graph to determine its domain and range.
$$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$$

A) Domain: $( - \infty , \infty )$
Range: $( - \infty , - 2 ]$ or $[ 2 , \infty )$
B) Domain: $( - \infty , \infty )$
Range: $( - \infty , - 2 ]$ and $[ 2 , \infty )$
C) Domain: $( - \infty , - 2 ]$ or $[ 2 , \infty )$
Range: $( - \infty , \infty )$
D) Domain: $( - \infty , - 2 ]$ and $[ 2 , \infty )$
Range: $( - \infty , \infty )$

Question 79

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
$$y ^ { 2 } = 24 x$$

A) focus: $( 6,0 )$
directrix: $x = - 6$
B) focus: $( 0,6 )$
directrix: $y = - 6$
C) focus: $( 6,0 )$
directrix: $x = 6$
D) focus: $( 0 , - 6 )$
directrix: $y = - 6$

Question 80

Graph Parabolas with Vertices at the Origin
Find the focus and directrix of the parabola with the given equation.
$$x ^ { 2 } = 11 y$$

A)

B)

C)

D)