Question 1

Find the center, foci, and vertices of the ellipse.
-$$\frac { ( x - 2 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  center at $( - 3,2 )$
foci at $( - 3 + 3 \sqrt { 3 } , 2 ) , ( - 3 - 3 \sqrt { 3 } , 2 )$
vertices at $( - 4 , - 3 ) , ( 8 , - 3 )$ 
B)  center at $( 2 , - 3 )$
foci at $( 2 + 3 \sqrt { 3 } , 2 ) , ( 2 - 3 \sqrt { 3 } , 2 )$
vertices at $( 6 , - 3 ) , ( - 6 , - 3 )$ 
C)  center at $( 2 , - 3 )$
foci at $( - 3 \sqrt { 3 } , - 3 ) , ( 3 \sqrt { 3 } , - 3 )$
vertices at $( 6 , - 3 ) , ( - 6 , - 3 )$ 
D)  center at $( 2 , - 3 )$
foci at $( 2 + 3 \sqrt { 3 } , - 3 ) , ( 2 - 3 \sqrt { 3 } , - 3 )$
vertices at $( - 4 , - 3 ) , ( 8 , - 3 )$ 
A)  center at $( - 3,2 )$
foci at $( - 3 + 3 \sqrt { 3 } , 2 ) , ( - 3 - 3 \sqrt { 3 } , 2 )$
vertices at $( - 4 , - 3 ) , ( 8 , - 3 )$ 
B)  center at $( 2 , - 3 )$
foci at $( 2 + 3 \sqrt { 3 } , 2 ) , ( 2 - 3 \sqrt { 3 } , 2 )$
vertices at $( 6 , - 3 ) , ( - 6 , - 3 )$ 
C)  center at $( 2 , - 3 )$
foci at $( - 3 \sqrt { 3 } , - 3 ) , ( 3 \sqrt { 3 } , - 3 )$
vertices at $( 6 , - 3 ) , ( - 6 , - 3 )$ 
D)  center at $( 2 , - 3 )$
foci at $( 2 + 3 \sqrt { 3 } , - 3 ) , ( 2 - 3 \sqrt { 3 } , - 3 )$
vertices at $( - 4 , - 3 ) , ( 8 , - 3 )$

Question 2

Graph the hyperbola.
-$$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Find an equation for the ellipse described.
-Center at (0, 0); focus at (5, 0); vertex at (8, 0)

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 39 } = 1$ 
D)  $\frac { x ^ { 2 } } { 39 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 39 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 39 } = 1$ 
D)  $\frac { x ^ { 2 } } { 39 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 4

Convert the equation to the standard form for a hyperbola by completing the square.
-$$4 y ^ { 2 } - 25 x ^ { 2 } + 8 y - 50 x - 121 = 0$$

Accepted Answer

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

Question 5

Graph the equation.
-$(y+2)^{2}=-5(x-1)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Find the equation in standard form of the parabola described.
-The focus has coordinates (0, 19), and the equation of the directrix is y = -19.

Accepted Answer

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

Question 7

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

Accepted Answer

A)  foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$
  
B)  foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$
  
C)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
D)  foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$
  
A)  foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$
  
B)  foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$
  
C)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
D)  foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$

Question 8

Solve the problem.
-A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

Accepted Answer

A) 0.6 ft 
B) 1.3 ft 
C) 5.3 ft 
D) 4 ft 
A) 0.6 ft 
B) 1.3 ft 
C) 5.3 ft 
D) 4 ft

Question 9

Find an equation for the ellipse described.
-Center at (-4, 5); focus at (-6, 5); contains the point (-9, 5)

Accepted Answer

A)  $\frac { ( x + 5 ) ^ { 2 } } { 21 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x + 5 ) ^ { 2 } } { 25 } + \frac { ( y - 4 ) ^ { 2 } } { 21 } = 1$ 
C) $\frac { ( x + 4 ) ^ { 2 } } { 21 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y - 5 ) ^ { 2 } } { 21 } = 1$ 
A)  $\frac { ( x + 5 ) ^ { 2 } } { 21 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( x + 5 ) ^ { 2 } } { 25 } + \frac { ( y - 4 ) ^ { 2 } } { 21 } = 1$ 
C) $\frac { ( x + 4 ) ^ { 2 } } { 21 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y - 5 ) ^ { 2 } } { 21 } = 1$

Question 10

Graph the hyperbola.
-$25 x^{2}-4 y^{2}=100$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Graph the equation.
-$$( x - 2 ) ^ { 2 } = 7 ( y + 2 )$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Find the equation in standard form of the parabola described.
-The vertex has coordinates (6, 9), and the focus has coordinates (7, 9).

Accepted Answer

A)  $( y - 9 ) ^ { 2 } = - 4 ( x - 6 )$ 
B)  $( x - 9 ) ^ { 2 } = 8 ( y - 9 )$ 
C)  $( x - 9 ) ^ { 2 } = - 8 ( y - 9 )$ 
D)  $( y - 9 ) ^ { 2 } = 4 ( x - 6 )$ 
A)  $( y - 9 ) ^ { 2 } = - 4 ( x - 6 )$ 
B)  $( x - 9 ) ^ { 2 } = 8 ( y - 9 )$ 
C)  $( x - 9 ) ^ { 2 } = - 8 ( y - 9 )$ 
D)  $( y - 9 ) ^ { 2 } = 4 ( x - 6 )$

Question 13

Graph the equation.
-$$\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

Graph the ellipse and locate the foci.
-$$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$$

Accepted Answer

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 $( - 2 \sqrt { 3 } , 0 )$
  
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 15

Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$16 x ^ { 2 } - 100 y ^ { 2 } = 1600$$

Accepted Answer

A)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( 0 , - 2 \sqrt { 29 } ) , ( 0,2 \sqrt { 29 } )$ 
B)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 21 } , 0 ) , ( 2 \sqrt { 21 } , 0 )$ 
C)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 2 \sqrt { 29 } , 0 ) , ( 2 \sqrt { 29 } , 0 )$ 
D)  center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 29 } , 0 ) , ( 2 \sqrt { 29 } , 0 )$ 
A)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( 0 , - 10 ) , ( 0,10 )$
foci: $( 0 , - 2 \sqrt { 29 } ) , ( 0,2 \sqrt { 29 } )$ 
B)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 21 } , 0 ) , ( 2 \sqrt { 21 } , 0 )$ 
C)  center at $( 0,0 )$
transverse axis is $x$-axis
vertices: $( - 4,0 ) , ( 4,0 )$
foci: $( - 2 \sqrt { 29 } , 0 ) , ( 2 \sqrt { 29 } , 0 )$ 
D)  center at $( 0,0 )$
transverse axis is $\mathrm { x }$-axis
vertices: $( - 10,0 ) , ( 10,0 )$
foci: $( - 2 \sqrt { 29 } , 0 ) , ( 2 \sqrt { 29 } , 0 )$

Question 16

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$( x - 1 ) ^ { 2 } - 4 ( y - 2 ) ^ { 2 } = 4$$

Accepted Answer

A)  center at $( 1,2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( 1,0 )$ and $( 1,4 )$,
foci at $( 1,2 - \sqrt { 5 } )$ and $( 1,2 + \sqrt { 5 } )$,
asymptotes of $y + 2 = - 2 ( x + 1 )$ and $y + 2 = 2 ( x + 1 )$ 
B)  center at $( 1,2 )$
transverse axis is parallel to $x$-axis
vertices at $( 0,2 )$ and $( 2,2 )$
foci at $( 1 - \sqrt { 5 } , 2 )$ and $( 1 + \sqrt { 5 } , 2 )$
asymptotes of $y - 2 = - 2 ( x - 1 )$ and $y - 2 = 2 ( x - 1 )$ 
C)  center at $( 1,2 )$
transverse axis is parallel to $x$-axis
vertices at $( - 1,2 )$ and $( 3,2 )$
foci at $( 1 - \sqrt { 5 } , 2 )$ and $( 1 + \sqrt { 5 } , 2 )$
asymptotes of $y - 2 = - \frac { 1 } { 2 } ( x - 1 )$ and $y - 2 = \frac { 1 } { 2 } ( x - 1 )$ 
D)  center at $( 2,1 )$
transverse axis is parallel to $x$-axis
vertices at $( 0,1 )$ and $( 4,1 )$
foci at $( 2 - \sqrt { 5 } , 1 )$ and $( 2 + \sqrt { 5 } , 1 )$
asymptotes of $y - 1 = - \frac { 1 } { 2 } ( x - 2 )$ and $y - 1 = \frac { 1 } { 2 } ( x - 2 )$ 
A)  center at $( 1,2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( 1,0 )$ and $( 1,4 )$,
foci at $( 1,2 - \sqrt { 5 } )$ and $( 1,2 + \sqrt { 5 } )$,
asymptotes of $y + 2 = - 2 ( x + 1 )$ and $y + 2 = 2 ( x + 1 )$ 
B)  center at $( 1,2 )$
transverse axis is parallel to $x$-axis
vertices at $( 0,2 )$ and $( 2,2 )$
foci at $( 1 - \sqrt { 5 } , 2 )$ and $( 1 + \sqrt { 5 } , 2 )$
asymptotes of $y - 2 = - 2 ( x - 1 )$ and $y - 2 = 2 ( x - 1 )$ 
C)  center at $( 1,2 )$
transverse axis is parallel to $x$-axis
vertices at $( - 1,2 )$ and $( 3,2 )$
foci at $( 1 - \sqrt { 5 } , 2 )$ and $( 1 + \sqrt { 5 } , 2 )$
asymptotes of $y - 2 = - \frac { 1 } { 2 } ( x - 1 )$ and $y - 2 = \frac { 1 } { 2 } ( x - 1 )$ 
D)  center at $( 2,1 )$
transverse axis is parallel to $x$-axis
vertices at $( 0,1 )$ and $( 4,1 )$
foci at $( 2 - \sqrt { 5 } , 1 )$ and $( 2 + \sqrt { 5 } , 1 )$
asymptotes of $y - 1 = - \frac { 1 } { 2 } ( x - 2 )$ and $y - 1 = \frac { 1 } { 2 } ( x - 2 )$

Question 17

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$\frac { ( x + 4 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$$

Accepted Answer

A)  center at $( - 4 , - 3 )$
transverse axis is parallel to $x$-axis
vertices at $( - 10 , - 3 )$ and $( 2 , - 3 )$
foci at $( - 4 - 2 \sqrt { 13 } , - 3 )$ and $( - 4 + 2 \sqrt { 13 } , - 3 )$
asymptotes of $y + 3 = - \frac { 2 } { 3 } ( x + 4 )$ and $y + 3 = \frac { 2 } { 3 } ( x + 4 )$ 
B)  center at $( - 4 , - 3 )$
transverse axis is parallel to $x$-axis
vertices at $( - 8 , - 3 )$ and $( 0 , - 3 )$
foci at $( - 4 - 2 \sqrt { 13 } , - 3 )$ and $( - 4 + 2 \sqrt { 13 } , - 3 )$
asymptotes of $y + 3 = - \frac { 3 } { 2 } ( x + 4 )$ and $y + 3 = \frac { 3 } { 2 } ( x + 4 )$ 
C)  center at $( - 3 , - 4 )$
transverse axis is parallel to $x$-axis
vertices at $( - 7 , - 4 )$ and $( 1 , - 4 )$
foci at $( - 3 - 2 \sqrt { 13 } , - 4 )$ and $( - 3 + 2 \sqrt { 13 } , - 4 )$
asymptotes of $y + 4 = - \frac { 3 } { 2 } ( x + 3 )$ and $y + 4 = \frac { 3 } { 2 } ( x + 3 )$ 
D)  center at $( - 4 , - 3 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( - 4 , - 7 )$ and $( - 4,1 )$
foci at $( - 4 , - 3 - 2 \sqrt { 13 } )$ and $( - 4 , - 3 + 2 \sqrt { 13 } )$
asymptotes of $y - 3 = - \frac { 2 } { 3 } ( x - 4 )$ and $y - 3 = \frac { 2 } { 3 } ( x - 4 )$ 
A)  center at $( - 4 , - 3 )$
transverse axis is parallel to $x$-axis
vertices at $( - 10 , - 3 )$ and $( 2 , - 3 )$
foci at $( - 4 - 2 \sqrt { 13 } , - 3 )$ and $( - 4 + 2 \sqrt { 13 } , - 3 )$
asymptotes of $y + 3 = - \frac { 2 } { 3 } ( x + 4 )$ and $y + 3 = \frac { 2 } { 3 } ( x + 4 )$ 
B)  center at $( - 4 , - 3 )$
transverse axis is parallel to $x$-axis
vertices at $( - 8 , - 3 )$ and $( 0 , - 3 )$
foci at $( - 4 - 2 \sqrt { 13 } , - 3 )$ and $( - 4 + 2 \sqrt { 13 } , - 3 )$
asymptotes of $y + 3 = - \frac { 3 } { 2 } ( x + 4 )$ and $y + 3 = \frac { 3 } { 2 } ( x + 4 )$ 
C)  center at $( - 3 , - 4 )$
transverse axis is parallel to $x$-axis
vertices at $( - 7 , - 4 )$ and $( 1 , - 4 )$
foci at $( - 3 - 2 \sqrt { 13 } , - 4 )$ and $( - 3 + 2 \sqrt { 13 } , - 4 )$
asymptotes of $y + 4 = - \frac { 3 } { 2 } ( x + 3 )$ and $y + 4 = \frac { 3 } { 2 } ( x + 3 )$ 
D)  center at $( - 4 , - 3 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices at $( - 4 , - 7 )$ and $( - 4,1 )$
foci at $( - 4 , - 3 - 2 \sqrt { 13 } )$ and $( - 4 , - 3 + 2 \sqrt { 13 } )$
asymptotes of $y - 3 = - \frac { 2 } { 3 } ( x - 4 )$ and $y - 3 = \frac { 2 } { 3 } ( x - 4 )$

Question 18

Graph the equation.
-$y^{2}=20 x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y - 4 ) ^ { 2 } = - 16 ( x - 1 )$$

Accepted Answer

A)  vertex: $( 1,4 )$
focus: $( - 3,4 )$
directrix: $x = 5$ 
B)  vertex: $( - 1 , - 4 )$
focus: $( - 5 , - 4 )$
directrix: $x = 3$ 
C)  vertex: $( 1,4 )$
focus: $( 5,4 )$
directrix: $x = - 3$ 
D)  vertex: $( 4,1 )$
focus: $( 0,1 )$
directrix: $x = 8$ 
A)  vertex: $( 1,4 )$
focus: $( - 3,4 )$
directrix: $x = 5$ 
B)  vertex: $( - 1 , - 4 )$
focus: $( - 5 , - 4 )$
directrix: $x = 3$ 
C)  vertex: $( 1,4 )$
focus: $( 5,4 )$
directrix: $x = - 3$ 
D)  vertex: $( 4,1 )$
focus: $( 0,1 )$
directrix: $x = 8$

Question 20

Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 121 } = 1$$

Accepted Answer

A)  center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 2 ) , ( 0,2 )$ 
oci: $( 0 , - 5 \sqrt { 5 } ) , ( 0,5 \sqrt { 5 } )$ 
B)  center at $( 0,0 )$
 transverse axis is $y$-axis 
vertices: $( - 2,0 ) , ( 2,0 )$ f
foci: $( - 11,0 ) , ( 11,0 )$ 
C)  center at $( 0,0 )$
transverse axis is $y$-axis
 vertices: $( 0 , - 2 ) , ( 0,2 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$ 
D)  center at $( 0,0 )$
 transverse axis is $x$-axis 
vertices: $( - 11,0 ) , ( 11,0 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$ 
A)  center at $( 0,0 )$
transverse axis is $\mathrm { y }$-axis
vertices: $( 0 , - 2 ) , ( 0,2 )$ 
oci: $( 0 , - 5 \sqrt { 5 } ) , ( 0,5 \sqrt { 5 } )$ 
B)  center at $( 0,0 )$
 transverse axis is $y$-axis 
vertices: $( - 2,0 ) , ( 2,0 )$ f
foci: $( - 11,0 ) , ( 11,0 )$ 
C)  center at $( 0,0 )$
transverse axis is $y$-axis
 vertices: $( 0 , - 2 ) , ( 0,2 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$ 
D)  center at $( 0,0 )$
 transverse axis is $x$-axis 
vertices: $( - 11,0 ) , ( 11,0 )$
foci: $( - 5 \sqrt { 5 } , 0 ) , ( 5 \sqrt { 5 } , 0 )$

Find the center, foci, and vertices of the ellipse. - $\frac { ( x - 2 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$

Graph the hyperbola. - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$

Find an equation for the ellipse described. -Center at (0, 0); focus at (5, 0); vertex at (8, 0)

Convert the equation to the standard form for a hyperbola by completing the square. - $4 y ^ { 2 } - 25 x ^ { 2 } + 8 y - 50 x - 121 = 0$

Graph the equation. - $(y+2)^{2}=-5(x-1)$ $Graph the equation. - (y+2)^{2}=-5(x-1)$

Find the equation in standard form of the parabola described. -The focus has coordinates (0, 19), and the equation of the directrix is y = -19.

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

Solve the problem. -A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

Find an equation for the ellipse described. -Center at (-4, 5); focus at (-6, 5); contains the point (-9, 5)

Graph the hyperbola. - $25 x^{2}-4 y^{2}=100$ $Graph the hyperbola. - 25 x^{2}-4 y^{2}=100$

Graph the equation. - $( x - 2 ) ^ { 2 } = 7 ( y + 2 )$ $Graph the equation. - ( x - 2 ) ^ { 2 } = 7 ( y + 2 )$

Find the equation in standard form of the parabola described. -The vertex has coordinates (6, 9), and the focus has coordinates (7, 9).

Graph the equation. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ $Graph the equation. - \frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Find the center, transverse axis, vertices, and foci of the hyperbola. - $16 x ^ { 2 } - 100 y ^ { 2 } = 1600$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $( x - 1 ) ^ { 2 } - 4 ( y - 2 ) ^ { 2 } = 4$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { ( x + 4 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$

Graph the equation. - $y^{2}=20 x$ $Graph the equation. - y^{2}=20 x$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y - 4 ) ^ { 2 } = - 16 ( x - 1 )$

Find the center, transverse axis, vertices, and foci of the hyperbola. - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 121 } = 1$

Equations, Inequalities, and Applications

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Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Systems of Equations and Inequalities

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Math Exercises: Sets, Intervals, Absolute Value, and Properties

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Exam 6: Conic Sections

Find the center, foci, and vertices of the ellipse. - (x−2)236+(y+3)29=1\frac { ( x - 2 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 136(x−2)2​+9(y+3)2​=1

Graph the hyperbola. - y24−x29=1\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 14y2​−9x2​=1

Find an equation for the ellipse described. -Center at (0, 0); focus at (5, 0); vertex at (8, 0)

Convert the equation to the standard form for a hyperbola by completing the square. - 4y2−25x2+8y−50x−121=04 y ^ { 2 } - 25 x ^ { 2 } + 8 y - 50 x - 121 = 04y2−25x2+8y−50x−121=0

Graph the equation. - (y+2)2=−5(x−1)(y+2)^{2}=-5(x-1)(y+2)2=−5(x−1)

Find the equation in standard form of the parabola described. -The focus has coordinates (0, 19), and the equation of the directrix is y = -19.

Graph the ellipse and locate the foci. - 4x2+9y2=364 x ^ { 2 } + 9 y ^ { 2 } = 364x2+9y2=36

Solve the problem. -A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

Find an equation for the ellipse described. -Center at (-4, 5); focus at (-6, 5); contains the point (-9, 5)

Graph the hyperbola. - 25x2−4y2=10025 x^{2}-4 y^{2}=10025x2−4y2=100

Graph the equation. - (x−2)2=7(y+2)( x - 2 ) ^ { 2 } = 7 ( y + 2 )(x−2)2=7(y+2)

Find the equation in standard form of the parabola described. -The vertex has coordinates (6, 9), and the focus has coordinates (7, 9).

Graph the equation. - (x+2)29+(y−2)216=1\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 19(x+2)2​+16(y−2)2​=1

Graph the ellipse and locate the foci. - x29+y24=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 19x2​+4y2​=1

Find the center, transverse axis, vertices, and foci of the hyperbola. - 16x2−100y2=160016 x ^ { 2 } - 100 y ^ { 2 } = 160016x2−100y2=1600

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - (x−1)2−4(y−2)2=4( x - 1 ) ^ { 2 } - 4 ( y - 2 ) ^ { 2 } = 4(x−1)2−4(y−2)2=4

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - (x+4)216−(y+3)236=1\frac { ( x + 4 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 36 } = 116(x+4)2​−36(y+3)2​=1

Graph the equation. - y2=20xy^{2}=20 xy2=20x

Find the vertex, focus, and directrix of the parabola with the given equation. - (y−4)2=−16(x−1)( y - 4 ) ^ { 2 } = - 16 ( x - 1 )(y−4)2=−16(x−1)

Find the center, transverse axis, vertices, and foci of the hyperbola. - y24−x2121=1\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 121 } = 14y2​−121x2​=1

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Systems of Equations and Inequalities

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Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

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Find the center, foci, and vertices of the ellipse. - $\frac { ( x - 2 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$

Graph the hyperbola. - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 9 } = 1$

Convert the equation to the standard form for a hyperbola by completing the square. - $4 y ^ { 2 } - 25 x ^ { 2 } + 8 y - 50 x - 121 = 0$

Graph the equation. - $(y+2)^{2}=-5(x-1)$ $Graph the equation. - (y+2)^{2}=-5(x-1)$

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

Graph the hyperbola. - $25 x^{2}-4 y^{2}=100$ $Graph the hyperbola. - 25 x^{2}-4 y^{2}=100$

Graph the equation. - $( x - 2 ) ^ { 2 } = 7 ( y + 2 )$ $Graph the equation. - ( x - 2 ) ^ { 2 } = 7 ( y + 2 )$

Graph the equation. - $\frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$ $Graph the equation. - \frac { ( x + 2 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 16 } = 1$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ $Graph the ellipse and locate the foci. - \frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$

Find the center, transverse axis, vertices, and foci of the hyperbola. - $16 x ^ { 2 } - 100 y ^ { 2 } = 1600$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $( x - 1 ) ^ { 2 } - 4 ( y - 2 ) ^ { 2 } = 4$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { ( x + 4 ) ^ { 2 } } { 16 } - \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$

Graph the equation. - $y^{2}=20 x$ $Graph the equation. - y^{2}=20 x$

Find the vertex, focus, and directrix of the parabola with the given equation. - $( y - 4 ) ^ { 2 } = - 16 ( x - 1 )$

Find the center, transverse axis, vertices, and foci of the hyperbola. - $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 121 } = 1$