Question 1

Graph the hyperbola.
-$(y-1)^{2}-4(x-1)^{2}=4$

Accepted Answer

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

Question 2

Graph the equation.
-$$4 ( x - 2 ) ^ { 2 } + 16 ( y + 1 ) ^ { 2 } = 64$$

Accepted Answer

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

Question 3

Find an equation for the ellipse described.
-Foci at (1, 4)and (7, 4); length of major axis is 10

Accepted Answer

A)  $\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 4 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( y + 4 ) ^ { 2 } } { 25 } + \frac { ( x - 4 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 4 ) ^ { 2 } } { 16 } = 1$ 
A)  $\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 4 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( y + 4 ) ^ { 2 } } { 25 } + \frac { ( x - 4 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 4 ) ^ { 2 } } { 16 } = 1$ C

Question 4

Convert the equation to the standard form for an ellipse by completing the square.
-$$16 x ^ { 2 } + 4 y ^ { 2 } + 32 x + 24 y - 12 = 0$$

Accepted Answer

A)  $\frac { ( x + 3 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( x + 3 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$

Question 5

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

Accepted Answer

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

Question 6

Solve the problem.
-A comet follows the hyperbolic path described by $\frac { x ^ { 2 } } { 10 } - \frac { y ^ { 2 } } { 24 } = 1$, where $x$ and $y$ are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Accepted Answer

A) 5.8 million miles 
B) 34 million miles 
C) 3.2 million miles 
D) 2.6 million miles 
A) 5.8 million miles 
B) 34 million miles 
C) 3.2 million miles 
D) 2.6 million miles

Question 7

Graph the hyperbola.
-$36 y^{2}=9 x^{2}+324$

Accepted Answer

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

Question 8

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$( y + 2 ) ^ { 2 } - 9 ( x - 4 ) ^ { 2 } = 9$$

Accepted Answer

A)  center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 4 , - 5 )$ and $( 4,1 )$
foci: $( 4 , - 2 - \sqrt { 10 } )$ and $( 4 , - 2 + \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$ 
B)  center: $( - 4,2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( - 4 , - 1 )$ and $( - 4,5 )$
foci: $( - 4,2 - \sqrt { 10 } )$ and $( - 4,2 + \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$ 
C)  center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 5 , - 4 )$ and $( 5,2 )$
foci: $( 5 , - 1 - \sqrt { 10 } )$ and $( 5 , - 1 + \sqrt { 10 } )$
asymptotes of $y + 2 = - \frac { 1 } { 3 } ( x - 4 )$ and $y + 2 = \frac { 1 } { 3 } ( x - 4 )$ 
D)  center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { x }$-axis
vertices: $( - 4 , - 3 )$ and $( 4,3 )$
foci: $( 4 , - \sqrt { 10 } )$ and $( 4 , \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$ 
A)  center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 4 , - 5 )$ and $( 4,1 )$
foci: $( 4 , - 2 - \sqrt { 10 } )$ and $( 4 , - 2 + \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$ 
B)  center: $( - 4,2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( - 4 , - 1 )$ and $( - 4,5 )$
foci: $( - 4,2 - \sqrt { 10 } )$ and $( - 4,2 + \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$ 
C)  center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 5 , - 4 )$ and $( 5,2 )$
foci: $( 5 , - 1 - \sqrt { 10 } )$ and $( 5 , - 1 + \sqrt { 10 } )$
asymptotes of $y + 2 = - \frac { 1 } { 3 } ( x - 4 )$ and $y + 2 = \frac { 1 } { 3 } ( x - 4 )$ 
D)  center: $( 4 , - 2 )$
transverse axis is parallel to $\mathrm { x }$-axis
vertices: $( - 4 , - 3 )$ and $( 4,3 )$
foci: $( 4 , - \sqrt { 10 } )$ and $( 4 , \sqrt { 10 } )$
asymptotes of $y + 2 = - 3 ( x - 4 )$ and $y + 2 = 3 ( x - 4 )$

Question 9

Convert the equation to the standard form for an ellipse by completing the square.
-$$4 x ^ { 2 } + 25 y ^ { 2 } - 8 x + 150 y + 129 = 0$$

Accepted Answer

A)  $\frac { ( x + 3 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 25 } + \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( x + 3 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( x + 1 ) ^ { 2 } } { 25 } + \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x - 1 ) ^ { 2 } } { 4 } + \frac { ( y + 3 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 1 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 4 } = 1$

Question 10

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
-$$\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 49 } = 1$$

Accepted Answer

A)  center: $( 3,1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 3,1 - \sqrt { 53 } )$ and $( 3,1 + \sqrt { 53 } )$;
foci: $( 3 , - 1 )$ and $( 3,3 )$
asymptotes of $y - 1 = - \frac { 7 } { 2 } ( x - 3 )$ and $y - 1 = \frac { 7 } { 2 } ( x - 3 )$ 
B)  center: $( 3,1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 1,0 )$ and $( 4,4 )$
foci: $( 1,2 - \sqrt { 53 } )$ and $( 4,2 + \sqrt { 53 } )$
asymptotes of $y - 1 = - \frac { 7 } { 2 } ( x - 3 )$ and $y - 1 = \frac { 7 } { 2 } ( x - 3 )$ 
C)  center: $( 3,1 )$
transverse axis is parallel to $y$-axis
vertices: $( 3 , - 1 )$ and $( 3,3 )$
foci: $( 3,1 - \sqrt { 53 } )$ and $( 3,1 + \sqrt { 53 } )$
asymptotes of $\mathrm { y } - 1 = - \frac { 2 } { 7 } ( x - 3 )$ and $y - 1 = \frac { 2 } { 7 } ( x - 3 )$ 
D)  center: $( - 3 , - 1 )$
transverse axis is parallel to $x$-axis
vertices: $( - 3 , - 3 )$ and $( - 3,1 )$
foci: $( - 3 , - 1 - \sqrt { 53 } )$ and $( - 3 , - 1 + \sqrt { 53 } )$
asymptotes of $y - 1 = - \frac { 2 } { 7 } ( x - 3 )$ and $y - 1 = \frac { 2 } { 7 } ( x - 3 )$ 
A)  center: $( 3,1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 3,1 - \sqrt { 53 } )$ and $( 3,1 + \sqrt { 53 } )$;
foci: $( 3 , - 1 )$ and $( 3,3 )$
asymptotes of $y - 1 = - \frac { 7 } { 2 } ( x - 3 )$ and $y - 1 = \frac { 7 } { 2 } ( x - 3 )$ 
B)  center: $( 3,1 )$
transverse axis is parallel to $\mathrm { y }$-axis
vertices: $( 1,0 )$ and $( 4,4 )$
foci: $( 1,2 - \sqrt { 53 } )$ and $( 4,2 + \sqrt { 53 } )$
asymptotes of $y - 1 = - \frac { 7 } { 2 } ( x - 3 )$ and $y - 1 = \frac { 7 } { 2 } ( x - 3 )$ 
C)  center: $( 3,1 )$
transverse axis is parallel to $y$-axis
vertices: $( 3 , - 1 )$ and $( 3,3 )$
foci: $( 3,1 - \sqrt { 53 } )$ and $( 3,1 + \sqrt { 53 } )$
asymptotes of $\mathrm { y } - 1 = - \frac { 2 } { 7 } ( x - 3 )$ and $y - 1 = \frac { 2 } { 7 } ( x - 3 )$ 
D)  center: $( - 3 , - 1 )$
transverse axis is parallel to $x$-axis
vertices: $( - 3 , - 3 )$ and $( - 3,1 )$
foci: $( - 3 , - 1 - \sqrt { 53 } )$ and $( - 3 , - 1 + \sqrt { 53 } )$
asymptotes of $y - 1 = - \frac { 2 } { 7 } ( x - 3 )$ and $y - 1 = \frac { 2 } { 7 } ( x - 3 )$

Question 11

Graph the hyperbola.
-$\frac{x^{2}}{4}-\frac{y^{2}}{25}=1$

Accepted Answer

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

Question 12

Find the center, foci, and vertices of the ellipse.
-$$16 ( x + 1 ) ^ { 2 } + 9 ( y - 3 ) ^ { 2 } = 144$$

Accepted Answer

A)  center at $( - 1,3 )$
foci at $( - 1,3 - \sqrt { 7 } ) , ( - 1,3 + \sqrt { 7 } )$
vertices at $( - 1,7 ) , ( - 1 , - 1 )$ 
B)  center at $( 1,3 )$
foci at $( 1,3 - \sqrt { 7 } ) , ( 1,3 + \sqrt { 7 } )$
vertices at $( 1,7 ) , ( 1 , - 1 )$ 
C)  center at $( 0,3 )$
foci at $( 0,3 - \sqrt { 7 } ) , ( 0,3 + \sqrt { 7 } )$
vertices at $( 0,7 ) , ( 0 , - 1 )$ 
D)  center at $( 3 , - 1 )$
foci at $( 3 , - 1 - \sqrt { 7 } ) , ( 3 , - 1 + \sqrt { 7 } )$
vertices at $( 3,7 ) , ( 3 , - 1 )$ 
A)  center at $( - 1,3 )$
foci at $( - 1,3 - \sqrt { 7 } ) , ( - 1,3 + \sqrt { 7 } )$
vertices at $( - 1,7 ) , ( - 1 , - 1 )$ 
B)  center at $( 1,3 )$
foci at $( 1,3 - \sqrt { 7 } ) , ( 1,3 + \sqrt { 7 } )$
vertices at $( 1,7 ) , ( 1 , - 1 )$ 
C)  center at $( 0,3 )$
foci at $( 0,3 - \sqrt { 7 } ) , ( 0,3 + \sqrt { 7 } )$
vertices at $( 0,7 ) , ( 0 , - 1 )$ 
D)  center at $( 3 , - 1 )$
foci at $( 3 , - 1 - \sqrt { 7 } ) , ( 3 , - 1 + \sqrt { 7 } )$
vertices at $( 3,7 ) , ( 3 , - 1 )$

Question 13

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, 200 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?

Accepted Answer

A) 1284.52 feet 
B) 1072.57 feet 
C) 4449.72 feet 
D) 436.36 feet 
A) 1284.52 feet 
B) 1072.57 feet 
C) 4449.72 feet 
D) 436.36 feet

Question 14

Find the vertex, focus, and directrix of the parabola. Graph the equation.
-$(x+3)^{2}=-(y+2)$

Accepted Answer

A)  vertex: $( - 3 , - 2 )$
focus: $( - 3.25 , - 2 )$
directrix: $x = - 2.75$
  
B)  vertex: $( 3,2 )$
focus: $( 3,1.75 )$
directrix: $y = 2.25$
  
C)  vertex: $( 3,2 )$
focus: $( 2.75,2 )$
directrix: $x = 3.25$
  
D)  vertex: $( - 3 , - 2 )$
focus: $( - 3 , - 2.25 )$
directrix: $y = - 1.75$
  
A)  vertex: $( - 3 , - 2 )$
focus: $( - 3.25 , - 2 )$
directrix: $x = - 2.75$
  
B)  vertex: $( 3,2 )$
focus: $( 3,1.75 )$
directrix: $y = 2.25$
  
C)  vertex: $( 3,2 )$
focus: $( 2.75,2 )$
directrix: $x = 3.25$
  
D)  vertex: $( - 3 , - 2 )$
focus: $( - 3 , - 2.25 )$
directrix: $y = - 1.75$

Question 15

Find the center, foci, and vertices of the ellipse.
-$$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  center at $( 0,0 )$
foci at $( 0 , - 3 )$ and $( 0,3 )$
vertices at $( 0 , - 9 ) , ( 0,9 )$ 
B)  center at $( 0,0 )$
foci at $( 0 , - 6 \sqrt { 2 } )$ and $( 0,6 \sqrt { 2 } )$
vertices at $( 0 , - 9 ) , ( 0,9 )$ 
C)  center at $( 0,0 )$
foci at $( - 6 \sqrt { 2 } , 0 )$ and $( 6 \sqrt { 2 } , 0 )$
vertices at $( - 9,0 ) , ( 9,0 )$ 
D)  center at $( 0,0 )$
foci at $( - 9,0 )$ and $( 9,0 )$
vertices at $( - 81,0 ) , ( 81,0 )$ 
A)  center at $( 0,0 )$
foci at $( 0 , - 3 )$ and $( 0,3 )$
vertices at $( 0 , - 9 ) , ( 0,9 )$ 
B)  center at $( 0,0 )$
foci at $( 0 , - 6 \sqrt { 2 } )$ and $( 0,6 \sqrt { 2 } )$
vertices at $( 0 , - 9 ) , ( 0,9 )$ 
C)  center at $( 0,0 )$
foci at $( - 6 \sqrt { 2 } , 0 )$ and $( 6 \sqrt { 2 } , 0 )$
vertices at $( - 9,0 ) , ( 9,0 )$ 
D)  center at $( 0,0 )$
foci at $( - 9,0 )$ and $( 9,0 )$
vertices at $( - 81,0 ) , ( 81,0 )$

Question 16

Find the vertex, focus, and directrix of the parabola with the given equation.
-$x - 1 ) ^ { 2 } = 8 ( y + 3 )$

Accepted Answer

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

Question 17

Find the center, transverse axis, vertices, and foci of the hyperbola.
-$$\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  center at $( 0,0 )$
transverse axis is $y$-axis
vertices at $( 0 , - 11 )$ and $( 0,11 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$ 
B)  center at $( 0,0 )$
 transverse axis is $\mathrm { x }$-axis
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - 5,0 )$ and $( 5,0 )$ 
C)  center at $( 0,0 )$
transverse axis is $x$-axis 
vertices at $( - 5,0 )$ and $( 5,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$ 
D)  center at $( 0,0 )$
transverse axis is $x$-axis 
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$ 
A)  center at $( 0,0 )$
transverse axis is $y$-axis
vertices at $( 0 , - 11 )$ and $( 0,11 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$ 
B)  center at $( 0,0 )$
 transverse axis is $\mathrm { x }$-axis
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - 5,0 )$ and $( 5,0 )$ 
C)  center at $( 0,0 )$
transverse axis is $x$-axis 
vertices at $( - 5,0 )$ and $( 5,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$ 
D)  center at $( 0,0 )$
transverse axis is $x$-axis 
vertices at $( - 11,0 )$ and $( 11,0 )$
foci at $( - \sqrt { 146 } , 0 )$ and $( \sqrt { 146 } , 0 )$

Question 18

Find the vertex, focus, and directrix of the parabola. Graph the equation.
-$$x ^ { 2 } - 12 x = 12 y - 96$$

Accepted Answer

A)  vertex: $( 6,5 )$
focus: $( 3,5 )$
directrix: $x = 9$
  
B)  vertex: $( 6,5 )$
focus: $( 6,8 )$
directrix: $y = 2$

Question 19

Find an equation for the ellipse described.
-Foci at (0, -3)and (0, 3); length of the major axis is 12

Accepted Answer

A)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 27 } = 1$ 
B)  $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 6 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 36 } = 1$ 
A)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 27 } = 1$ 
B)  $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 6 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 36 } = 1$

Question 20

Find an equation for the hyperbola described.
-Focus at (3, 6); vertices at (8, 6)and (6, 6)

Accepted Answer

A)  $\frac { ( x - 7 ) ^ { 2 } } { 15 } - ( y - 6 ) ^ { 2 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 15 } - ( y - 7 ) ^ { 2 } = 1$ 
C)  $( x - 7 ) ^ { 2 } - \frac { ( y - 6 ) ^ { 2 } } { 15 } = 1$ 
D)  $( x - 6 ) ^ { 2 } - \frac { ( y - 7 ) ^ { 2 } } { 15 } = 1$ 
A)  $\frac { ( x - 7 ) ^ { 2 } } { 15 } - ( y - 6 ) ^ { 2 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 15 } - ( y - 7 ) ^ { 2 } = 1$ 
C)  $( x - 7 ) ^ { 2 } - \frac { ( y - 6 ) ^ { 2 } } { 15 } = 1$ 
D)  $( x - 6 ) ^ { 2 } - \frac { ( y - 7 ) ^ { 2 } } { 15 } = 1$

Graph the hyperbola. - $(y-1)^{2}-4(x-1)^{2}=4$ $Graph the hyperbola. - (y-1)^{2}-4(x-1)^{2}=4$

Graph the equation. - $4 ( x - 2 ) ^ { 2 } + 16 ( y + 1 ) ^ { 2 } = 64$ $Graph the equation. - 4 ( x - 2 ) ^ { 2 } + 16 ( y + 1 ) ^ { 2 } = 64$

Find an equation for the ellipse described. -Foci at (1, 4)and (7, 4); length of major axis is 10

Convert the equation to the standard form for an ellipse by completing the square. - $16 x ^ { 2 } + 4 y ^ { 2 } + 32 x + 24 y - 12 = 0$

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

Graph the hyperbola. - $36 y^{2}=9 x^{2}+324$ $Graph the hyperbola. - 36 y^{2}=9 x^{2}+324$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $( y + 2 ) ^ { 2 } - 9 ( x - 4 ) ^ { 2 } = 9$

Convert the equation to the standard form for an ellipse by completing the square. - $4 x ^ { 2 } + 25 y ^ { 2 } - 8 x + 150 y + 129 = 0$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 49 } = 1$

Graph the hyperbola. - $\frac{x^{2}}{4}-\frac{y^{2}}{25}=1$ $Graph the hyperbola. - \frac{x^{2}}{4}-\frac{y^{2}}{25}=1$

Find the center, foci, and vertices of the ellipse. - $16 ( x + 1 ) ^ { 2 } + 9 ( y - 3 ) ^ { 2 } = 144$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $(x+3)^{2}=-(y+2)$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - (x+3)^{2}=-(y+2)$

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$

Find the vertex, focus, and directrix of the parabola with the given equation. - $x - 1 ) ^ { 2 } = 8 ( y + 3 )$

Find the center, transverse axis, vertices, and foci of the hyperbola. - $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $x ^ { 2 } - 12 x = 12 y - 96$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - x ^ { 2 } - 12 x = 12 y - 96$

Find an equation for the ellipse described. -Foci at (0, -3)and (0, 3); length of the major axis is 12

Find an equation for the hyperbola described. -Focus at (3, 6); vertices at (8, 6)and (6, 6)

Equations, Inequalities, and Applications

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Exam 6: Conic Sections

Graph the hyperbola. - (y−1)2−4(x−1)2=4(y-1)^{2}-4(x-1)^{2}=4(y−1)2−4(x−1)2=4

Graph the equation. - 4(x−2)2+16(y+1)2=644 ( x - 2 ) ^ { 2 } + 16 ( y + 1 ) ^ { 2 } = 644(x−2)2+16(y+1)2=64

Find an equation for the ellipse described. -Foci at (1, 4)and (7, 4); length of major axis is 10

Convert the equation to the standard form for an ellipse by completing the square. - 16x2+4y2+32x+24y−12=016 x ^ { 2 } + 4 y ^ { 2 } + 32 x + 24 y - 12 = 016x2+4y2+32x+24y−12=0

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

Solve the problem. -A comet follows the hyperbolic path described by x210−y224=1\frac { x ^ { 2 } } { 10 } - \frac { y ^ { 2 } } { 24 } = 110x2​−24y2​=1 , where xxx and yyy are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Graph the hyperbola. - 36y2=9x2+32436 y^{2}=9 x^{2}+32436y2=9x2+324

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - (y+2)2−9(x−4)2=9( y + 2 ) ^ { 2 } - 9 ( x - 4 ) ^ { 2 } = 9(y+2)2−9(x−4)2=9

Convert the equation to the standard form for an ellipse by completing the square. - 4x2+25y2−8x+150y+129=04 x ^ { 2 } + 25 y ^ { 2 } - 8 x + 150 y + 129 = 04x2+25y2−8x+150y+129=0

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - (y−1)24−(x−3)249=1\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 49 } = 14(y−1)2​−49(x−3)2​=1

Graph the hyperbola. - x24−y225=1\frac{x^{2}}{4}-\frac{y^{2}}{25}=14x2​−25y2​=1

Find the center, foci, and vertices of the ellipse. - 16(x+1)2+9(y−3)2=14416 ( x + 1 ) ^ { 2 } + 9 ( y - 3 ) ^ { 2 } = 14416(x+1)2+9(y−3)2=144

Find the vertex, focus, and directrix of the parabola. Graph the equation. - (x+3)2=−(y+2)(x+3)^{2}=-(y+2)(x+3)2=−(y+2)

Find the center, foci, and vertices of the ellipse. - x281+y29=1\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 181x2​+9y2​=1

Find the vertex, focus, and directrix of the parabola with the given equation. - x−1)2=8(y+3)x - 1 ) ^ { 2 } = 8 ( y + 3 )x−1)2=8(y+3)

Find the center, transverse axis, vertices, and foci of the hyperbola. - x2121−y225=1\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1121x2​−25y2​=1

Find the vertex, focus, and directrix of the parabola. Graph the equation. - x2−12x=12y−96x ^ { 2 } - 12 x = 12 y - 96x2−12x=12y−96

Find an equation for the ellipse described. -Foci at (0, -3)and (0, 3); length of the major axis is 12

Find an equation for the hyperbola described. -Focus at (3, 6); vertices at (8, 6)and (6, 6)

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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Graph the hyperbola. - $(y-1)^{2}-4(x-1)^{2}=4$ $Graph the hyperbola. - (y-1)^{2}-4(x-1)^{2}=4$

Graph the equation. - $4 ( x - 2 ) ^ { 2 } + 16 ( y + 1 ) ^ { 2 } = 64$ $Graph the equation. - 4 ( x - 2 ) ^ { 2 } + 16 ( y + 1 ) ^ { 2 } = 64$

Convert the equation to the standard form for an ellipse by completing the square. - $16 x ^ { 2 } + 4 y ^ { 2 } + 32 x + 24 y - 12 = 0$

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

Graph the hyperbola. - $36 y^{2}=9 x^{2}+324$ $Graph the hyperbola. - 36 y^{2}=9 x^{2}+324$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $( y + 2 ) ^ { 2 } - 9 ( x - 4 ) ^ { 2 } = 9$

Convert the equation to the standard form for an ellipse by completing the square. - $4 x ^ { 2 } + 25 y ^ { 2 } - 8 x + 150 y + 129 = 0$

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola. - $\frac { ( y - 1 ) ^ { 2 } } { 4 } - \frac { ( x - 3 ) ^ { 2 } } { 49 } = 1$

Graph the hyperbola. - $\frac{x^{2}}{4}-\frac{y^{2}}{25}=1$ $Graph the hyperbola. - \frac{x^{2}}{4}-\frac{y^{2}}{25}=1$

Find the center, foci, and vertices of the ellipse. - $16 ( x + 1 ) ^ { 2 } + 9 ( y - 3 ) ^ { 2 } = 144$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $(x+3)^{2}=-(y+2)$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - (x+3)^{2}=-(y+2)$

Find the center, foci, and vertices of the ellipse. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 9 } = 1$

Find the vertex, focus, and directrix of the parabola with the given equation. - $x - 1 ) ^ { 2 } = 8 ( y + 3 )$

Find the center, transverse axis, vertices, and foci of the hyperbola. - $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 25 } = 1$

Find the vertex, focus, and directrix of the parabola. Graph the equation. - $x ^ { 2 } - 12 x = 12 y - 96$ $Find the vertex, focus, and directrix of the parabola. Graph the equation. - x ^ { 2 } - 12 x = 12 y - 96$