Question 1

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.
-$$y ^ { 2 } - 4 y - 6 x + 34 = 0$$

Accepted Answer

A)  $( y - 2 ) ^ { 2 } = 6 ( x - 5 )$ 
B)  $( y + 2 ) ^ { 2 } = 6 ( x - 5 )$ 
C)  $( y + 2 ) ^ { 2 } = - 6 ( x - 5 )$ 
D)  $( y - 2 ) ^ { 2 } = 6 ( x + 5 )$ 
A)  $( y - 2 ) ^ { 2 } = 6 ( x - 5 )$ 
B)  $( y + 2 ) ^ { 2 } = 6 ( x - 5 )$ 
C)  $( y + 2 ) ^ { 2 } = - 6 ( x - 5 )$ 
D)  $( y - 2 ) ^ { 2 } = 6 ( x + 5 )$

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.
-$$\begin{array} { l } 
x = ( y + 10 ) ^ { 2 } - 1 \
( x - 10 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 1
\end{array}$$

Accepted Answer

A)  $\{ ( 10 , - 10 ) \}$ 
B)  $\{ ( - 1 , - 10 ) \}$ 
C)  $\{ ( - 1 , - 10 ) , ( 10 , - 10 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( 10 , - 10 ) \}$ 
B)  $\{ ( - 1 , - 10 ) \}$ 
C)  $\{ ( - 1 , - 10 ) , ( 10 , - 10 ) \}$ 
D)  $\varnothing$

Question 3

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

Accepted Answer

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

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

Accepted Answer

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: $y = - 6$ 
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 5

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

Accepted Answer

A)  Asymptotes: $y = \pm x$
  
B)  Asymptotes: $y = \pm 3 x$
  
C)  Asymptotes: $y = \pm \frac { 1 } { 3 } x$
  
D)  Asymptotes: $y = \pm x$
  
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 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Graph Parabolas with Vertices Not at the Origin
Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( x - 2 ) ^ { 2 } = 7 ( y + 1 )$$

Accepted Answer

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

Question 9

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

Accepted Answer

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 $( - 2 \sqrt { 3 } , 0 )$
  
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 10

Graph Parabolas with Vertices Not at the Origin
Find the vertex, focus, and directrix of the parabola with the given equation.
-$$( y - 1 ) ^ { 2 } = 7 ( x + 1 )$$

Accepted Answer

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

Question 11

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

Accepted Answer

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: $( 0 , - \sqrt { 34 } ) , ( 0 , \sqrt { 34 } )$ 
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 12

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)

Accepted Answer

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)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 196 } = 1$ 
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)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 196 } = 1$

Question 13

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)

Accepted Answer

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)  $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 256 } = 1$ 
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 14

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

Accepted Answer

A)  Domain: $[ - 4,4 ]$
 Range: $[ - 2,2 ]$ 
B)  Domain: $[ - 2,2 ]$
Range: $[ - 4,4 ]$ 
C)  Domain: $( - 4,4 )$
Range: $( - 2,2 )$ 
D)  Domain: $[ - 4,4 ]$ 
$\text { Range: }(-\infty, \infty)$ 
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 15

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

Accepted Answer

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

Question 16

Write Equations of Hyperbolas in Standard Form
-Foci: (0, -5), (0, 5); vertices: (0, -3), (0, 3)

Accepted Answer

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)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$ 
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 17

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?

Accepted Answer

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

Question 18

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

Accepted Answer

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: $y = - 4$ 
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 19

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

Accepted Answer

A)  $\frac { ( y - 2 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( y - 2 ) ^ { 2 } } { 4 } - \frac { ( x + 2 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$ 
A)  $\frac { ( y - 2 ) ^ { 2 } } { 25 } - \frac { ( x + 2 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( y + 2 ) ^ { 2 } } { 25 } - \frac { ( x - 2 ) ^ { 2 } } { 4 } = 1$ 
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 20

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

Accepted Answer

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)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 16 } = 1$ 
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)  $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 16 } = 1$

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. - $y ^ { 2 } - 4 y - 6 x + 34 = 0$

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

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

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

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

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

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

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)

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)

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

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

Write Equations of Hyperbolas in Standard Form -Foci: (0, -5), (0, 5); vertices: (0, -3), (0, 3)

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

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

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

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Exam 7: Conic Sections

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. - y2−4y−6x+34=0y ^ { 2 } - 4 y - 6 x + 34 = 0y2−4y−6x+34=0

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. - x=(y+10-1 (x-10+(y+10=1

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

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - y2=24xy ^ { 2 } = 24 xy2=24x

Graph Hyperbolas Centered at the Origin Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes. - y=±x2−6y = \pm \sqrt { x ^ { 2 } - 6 }y=±x2−6​

Graph Ellipses Not Centered at the Origin - (x+2)216+(y+1)24=1\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 116(x+2)2​+4(y+1)2​=1

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

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - (x−2)2=7(y+1)( x - 2 ) ^ { 2 } = 7 ( y + 1 )(x−2)2=7(y+1)

Graph the ellipse and locate the foci. - 9x2+4y2=369 x ^ { 2 } + 4 y ^ { 2 } = 369x2+4y2=36

Graph Parabolas with Vertices Not at the Origin Find the vertex, focus, and directrix of the parabola with the given equation. - (y−1)2=7(x+1)( y - 1 ) ^ { 2 } = 7 ( x + 1 )(y−1)2=7(x+1)

Find the vertices and locate the foci for the hyperbola whose equation is given. - 25y2−9x2=22525 \mathrm { y } ^ { 2 } - 9 \mathrm { x } ^ { 2 } = 22525y2−9x2=225

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)

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)

Additional Concepts Use the relation's graph to determine its domain and range. - x216+y24=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 116x2​+4y2​=1

Graph the parabola. - x2=−20yx ^ { 2 } = - 20 yx2=−20y

Write Equations of Hyperbolas in Standard Form -Foci: (0, -5), (0, 5); vertices: (0, -3), (0, 3)

Graph Parabolas with Vertices at the Origin Find the focus and directrix of the parabola with the given equation. - x2=−16yx ^ { 2 } = - 16 yx2=−16y

Convert the equation to the standard form for a hyperbola by completing the square on x and y. - 4y2−25x2−16y−100x−184=04 y ^ { 2 } - 25 x ^ { 2 } - 16 y - 100 x - 184 = 04y2−25x2−16y−100x−184=0

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

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Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. - $y ^ { 2 } - 4 y - 6 x + 34 = 0$

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

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

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

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

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

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

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

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

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

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

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