Question 1

Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Vertex: $( 3 , - 7 )$; Focus: $( 3 , - 6 )$

Accepted Answer

A)  $( x - 3 ) ^ { 2 } = 4 ( y + 7 )$ 
B)  $( x - 3 ) ^ { 2 } = - 4 ( y + 7 )$ 
C)  $( y - 7 ) ^ { 2 } = 12 ( x + 3 )$ 
D)  $( y - 7 ) ^ { 2 } = - 12 ( x + 3 )$ 
A)  $( x - 3 ) ^ { 2 } = 4 ( y + 7 )$ 
B)  $( x - 3 ) ^ { 2 } = - 4 ( y + 7 )$ 
C)  $( y - 7 ) ^ { 2 } = 12 ( x + 3 )$ 
D)  $( y - 7 ) ^ { 2 } = - 12 ( x + 3 )$

Question 2

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.
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 9 \
x ^ { 2 } + y ^ { 2 } = 9
\end{array}$$

Accepted Answer

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

Question 3

Additional Concepts
Determine the direction in which the parabola opens, and the vertex.
-$$x = - ( y - 8 ) ^ { 2 } + 1$$

Accepted Answer

A)  Opens to left; $( 1,8 )$ 
B)  Opens to left; $( 1 , - 8 )$ 
C)  Opens to left; $( 8,1 )$ 
D)  Opens to right; $( 8,1 )$ 
A)  Opens to left; $( 1,8 )$ 
B)  Opens to left; $( 1 , - 8 )$ 
C)  Opens to left; $( 8,1 )$ 
D)  Opens to right; $( 8,1 )$

Question 4

Write Equations of Parabolas in Standard Form
Find the standard form of the equation of the parabola using the information given.
-Focus: $( - 19,0 )$; Directrix: $x = 19$

Accepted Answer

A)  $y ^ { 2 } = - 76 x$ 
B)  $y ^ { 2 } = 76 x$ 
C)  $y ^ { 2 } = - 19 x$ 
D)  $x ^ { 2 } = - 76 y$ 
A)  $y ^ { 2 } = - 76 x$ 
B)  $y ^ { 2 } = 76 x$ 
C)  $y ^ { 2 } = - 19 x$ 
D)  $x ^ { 2 } = - 76 y$

Question 5

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

Accepted Answer

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)  $\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y - 3 ) ^ { 2 } } { 25 } = 1$ 
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 6

Solve the problem.
-An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers
Are both 4 inches tall and stand 40 inches apart. At some point along the road from the lowest point of the
Cable, the cable is 0.36 inches above the roadway. Find the distance between that point and the base of the
Nearest tower.

Accepted Answer

A) 14 in. 
B) 5.8 in. 
C) 14.2 in. 
D) 6.2 in. 
A) 14 in. 
B) 5.8 in. 
C) 14.2 in. 
D) 6.2 in.

Question 7

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.

Accepted Answer

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. 
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 8

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.

Accepted Answer

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. 
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 9

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range.
-$$y ^ { 2 } - 12 y - x + 32 = 0$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 10

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

Accepted Answer

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 $( 0 , - 3 )$
  
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 11

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
-$$x ^ { 2 } - 4 x - 3 y - 5 = 0$$

Accepted Answer

A)  $( x - 2 ) ^ { 2 } = 3 ( y + 3 )$ 
B)  $( x + 2 ) ^ { 2 } = 3 ( y + 3 )$ 
C)  $( x + 2 ) ^ { 2 } = - 3 ( y + 3 )$ 
D)  $( x - 2 ) ^ { 2 } = 3 ( y - 3 )$ 
A)  $( x - 2 ) ^ { 2 } = 3 ( y + 3 )$ 
B)  $( x + 2 ) ^ { 2 } = 3 ( y + 3 )$ 
C)  $( x + 2 ) ^ { 2 } = - 3 ( y + 3 )$ 
D)  $( x - 2 ) ^ { 2 } = 3 ( y - 3 )$

Question 12

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

Accepted Answer

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)  $( x - 2 ) ^ { 2 } - \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
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 13

Write Equations of Hyperbolas in Standard Form
-Foci: (-5, 0), (5, 0); vertices: (-2, 0), (2, 0)

Accepted Answer

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)  $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 25 } = 1$ 
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 14

Write Equations of Ellipses in Standard Form
-

Accepted Answer

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 $( 7,0 )$ 
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 the ellipse and locate the foci.
-$$\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$$

Accepted Answer

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 $( 0 , - 7 )$
  
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 16

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);

Accepted Answer

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)  $\frac { ( x + 4 ) ^ { 2 } } { 4 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ 
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 17

Solve the problem.
-An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers
Are both 12.25 inches tall and stand 70 inches apart. Find the vertical distance from the roadway to the
Cable at a point on the road 17.5 inches from the lowest point of the cable.

Accepted Answer

A) 3.06 in. 
B) 12.25 in. 
C) 3.26 in. 
D) 2.86 in. 
A) 3.06 in. 
B) 12.25 in. 
C) 3.26 in. 
D) 2.86 in.

Question 18

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.
-$$\begin{array} { l } 
x = y ^ { 2 } - 2 \
x = y ^ { 2 } - 2 y
\end{array}$$

Accepted Answer

A)  $\{ ( - 1,1 ) \}$ 
B)  $\{ ( 1 , - 1 ) \}$ 
C)  $\{ ( 1,1 ) \}$ 
D)  $\{ ( - 1 , - 1 ) \}$ 
A)  $\{ ( - 1,1 ) \}$ 
B)  $\{ ( 1 , - 1 ) \}$ 
C)  $\{ ( 1,1 ) \}$ 
D)  $\{ ( - 1 , - 1 ) \}$

Question 19

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range.
-$$x = - ( y - 8 ) ^ { 2 } - 1$$

Accepted Answer

A)  Domain: $( - \infty , - 1 ]$
Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , - 1 )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$ 
Range: $( - \infty ,-1)$ Is the relation a function? 
A)  Domain: $( - \infty , - 1 ]$
Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , - 1 )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$ 
Range: $( - \infty ,-1)$ Is the relation a function?

Question 20

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

Accepted Answer

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 $( 4 , - 2 + \sqrt { 11 } )$ 
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 $( 4 , - 2 + \sqrt { 11 } )$

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Vertex: $( 3 , - 7 )$ ; Focus: $( 3 , - 6 )$

Additional Concepts Determine the direction in which the parabola opens, and the vertex. - $x = - ( y - 8 ) ^ { 2 } + 1$

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Focus: $( - 19,0 )$ ; Directrix: $x = 19$

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

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - $y ^ { 2 } - 12 y - x + 32 = 0$

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

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. - $x ^ { 2 } - 4 x - 3 y - 5 = 0$

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

Write Equations of Hyperbolas in Standard Form -Foci: (-5, 0), (5, 0); vertices: (-2, 0), (2, 0)

Write Equations of Ellipses in Standard Form -

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

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);

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - $x = - ( y - 8 ) ^ { 2 } - 1$

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

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Exam 7: Conic Sections

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Vertex: (3,−7)( 3 , - 7 )(3,−7) ; Focus: (3,−6)( 3 , - 6 )(3,−6)

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. - -=9 +=9

Additional Concepts Determine the direction in which the parabola opens, and the vertex. - x=−(y−8)2+1x = - ( y - 8 ) ^ { 2 } + 1x=−(y−8)2+1

Write Equations of Parabolas in Standard Form Find the standard form of the equation of the parabola using the information given. -Focus: (−19,0)( - 19,0 )(−19,0) ; Directrix: x=19x = 19x=19

Convert the equation to the standard form for an ellipse by completing the square on x and y. - 25x2+16y2−100x+96y−156=025 x ^ { 2 } + 16 y ^ { 2 } - 100 x + 96 y - 156 = 025x2+16y2−100x+96y−156=0

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. - y2−12y−x+32=0y ^ { 2 } - 12 y - x + 32 = 0y2−12y−x+32=0

Graph the ellipse and locate the foci. - x249+y240=1\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 40 } = 149x2​+40y2​=1

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. - x2−4x−3y−5=0x ^ { 2 } - 4 x - 3 y - 5 = 0x2−4x−3y−5=0

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - y2−16x2−4y+64x−76=0\mathrm { y } ^ { 2 } - 16 \mathrm { x } ^ { 2 } - 4 \mathrm { y } + 64 \mathrm { x } - 76 = 0y2−16x2−4y+64x−76=0