Question 1

Write an equation for the illustrated plane.
-

Accepted Answer

A)  $- 3 x - 3 y - 2 z = 6$ 
B)  $2 x + 2 y + 3 z = - 6$ 
C)  $2 x + 2 y + 3 z = 0$ 
D)  $3 x + 3 y + 2 z = 6$ 
A)  $- 3 x - 3 y - 2 z = 6$ 
B)  $2 x + 2 y + 3 z = - 6$ 
C)  $2 x + 2 y + 3 z = 0$ 
D)  $3 x + 3 y + 2 z = 6$

Question 2

Graph the ellipse.
-$\frac{(x+2)^{2}}{16}+\frac{(y-3)^{2}}{4}=1$

Accepted Answer

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

Question 3

Write an equation for the sphere with the given point as its center and the given number as its radius.
-$( 9,4,5 ) , 6$

Accepted Answer

A)  $( x + 9 ) ^ { 2 } + ( y + 4 ) ^ { 2 } + ( z + 5 ) ^ { 2 } = 6$ 
B)  $( x + 9 ) ^ { 2 } + ( y + 4 ) ^ { 2 } + ( z + 5 ) ^ { 2 } = 36$ 
C)  $( x - 9 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 6$ 
D)  $( x - 9 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 36$ 
A)  $( x + 9 ) ^ { 2 } + ( y + 4 ) ^ { 2 } + ( z + 5 ) ^ { 2 } = 6$ 
B)  $( x + 9 ) ^ { 2 } + ( y + 4 ) ^ { 2 } + ( z + 5 ) ^ { 2 } = 36$ 
C)  $( x - 9 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 6$ 
D)  $( x - 9 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + ( z - 5 ) ^ { 2 } = 36$

Question 4

Graph the parabola.
-$8 y=-x^{2}$

Accepted Answer

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

Question 5

Solve the problem.
- 
A radio telescope has a parabolic surface. If it is $9 \mathrm {~m}$ deep and $12 \mathrm {~m}$ wide, how far is the focus from the vertex?

Accepted Answer

A)  $4 \mathrm {~m}$ 
B)  $3 \mathrm {~m}$ 
C)  $1 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$ 
A)  $4 \mathrm {~m}$ 
B)  $3 \mathrm {~m}$ 
C)  $1 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$

Question 6

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.
-$$3 x ^ { 2 } + 6 x y + 3 y ^ { 2 } - 2 x + 4 y = 0$$

Accepted Answer

A)  Parabola 
B)  Ellipse 
C)  Hyperbola 
A)  Parabola 
B)  Ellipse 
C)  Hyperbola

Question 7

Find an equation in standard form for the ellipse that satisfies the given conditions.
-An ellipse with center at origin, length of major axis 14 and $y$-intercepts $( 0 , \pm 6 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 7 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 36 } = 1$ 
A)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 7 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 36 } = 1$

Question 8

Solve the problem.
- 
A building has an entry the shape of a parabolic arch $98 \mathrm { ft }$ high and $30 \mathrm { ft }$ wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Accepted Answer

A)  $x ^ { 2 } = - 2.3 y$ 
B)  $\mathrm { y } ^ { 2 } = - 9.2 \mathrm { x }$ 
C)  $x ^ { 2 } = - 9.2 y$ 
D)  $y ^ { 2 } = - 2.3 x$ 
A)  $x ^ { 2 } = - 2.3 y$ 
B)  $\mathrm { y } ^ { 2 } = - 9.2 \mathrm { x }$ 
C)  $x ^ { 2 } = - 9.2 y$ 
D)  $y ^ { 2 } = - 2.3 x$

Question 9

Find the vertex, focus, directrix, and focal width of the parabola.
-$$( x - 9 ) ^ { 2 } = - 8 ( y + 6 )$$

Accepted Answer

A)  Vertex: $( - 6,9 )$; Focus: $( - 8,9 )$; Directrix: $x = 11$; Focal width: 2 
B)  Vertex: $( - 9,6 )$; Focus: $( - 9 , - 2 )$; Directrix: $y = 14$; Focal width: 8 
C)  Vertex: $( - 6,9 )$; Focus: $( - 14,9 )$; Directrix: $x = 17$; Focal width: 8 
D)  Vertex: $( 9 , - 6 )$; Focus: $( 9 , - 8 )$; Directrix: $y = - 4$; Focal width: 8 
A)  Vertex: $( - 6,9 )$; Focus: $( - 8,9 )$; Directrix: $x = 11$; Focal width: 2 
B)  Vertex: $( - 9,6 )$; Focus: $( - 9 , - 2 )$; Directrix: $y = 14$; Focal width: 8 
C)  Vertex: $( - 6,9 )$; Focus: $( - 14,9 )$; Directrix: $x = 17$; Focal width: 8 
D)  Vertex: $( 9 , - 6 )$; Focus: $( 9 , - 8 )$; Directrix: $y = - 4$; Focal width: 8

Question 10

Find an equation in standard form for the ellipse that satisfies the given conditions.
-The vertical major axis is of length 8 , and the minor axis is of length 4 .

Accepted Answer

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

Question 11

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic.
-Directrix $x = - 8$, eccentricity 3

Accepted Answer

A)  $r = \frac { 24 } { 1 - 3 \cos \theta }$, hyperbola 
B)  $r = \frac { 24 } { 1 - 8 \cos \theta }$, hyperbola 
C)  $r = \frac { 8 } { 8 + \cos \theta }$, ellipse 
D)  $r = \frac { 3 } { 8 - 8 \cos \theta }$, parabola 
A)  $r = \frac { 24 } { 1 - 3 \cos \theta }$, hyperbola 
B)  $r = \frac { 24 } { 1 - 8 \cos \theta }$, hyperbola 
C)  $r = \frac { 8 } { 8 + \cos \theta }$, ellipse 
D)  $r = \frac { 3 } { 8 - 8 \cos \theta }$, parabola

Question 12

Find the vertex, focus, directrix, and focal width of the parabola.
-$$x = 8 y ^ { 2 }$$

Accepted Answer

A)  Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 32 } , 0 \right) ;$ Directrix: $x = \frac { 1 } { 32 } ;$ Focal width: 32 
B)  Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 8 } , 0 \right) ;$ Directrix: $x = - \frac { 1 } { 8 } ;$ Focal width: $0.13$ 
C)  Vertex: $( 0,0 )$; Focus: $\left( 0 , \frac { 1 } { 32 } \right) ;$ Directrix: $y = - \frac { 1 } { 32 }$; Focal width: 32 
D)  Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 32 } , 0 \right) ;$ Directrix: $x = - \frac { 1 } { 32 } ;$ Focal width: $0.13$ 
A)  Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 32 } , 0 \right) ;$ Directrix: $x = \frac { 1 } { 32 } ;$ Focal width: 32 
B)  Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 8 } , 0 \right) ;$ Directrix: $x = - \frac { 1 } { 8 } ;$ Focal width: $0.13$ 
C)  Vertex: $( 0,0 )$; Focus: $\left( 0 , \frac { 1 } { 32 } \right) ;$ Directrix: $y = - \frac { 1 } { 32 }$; Focal width: 32 
D)  Vertex: $( 0,0 )$; Focus: $\left( \frac { 1 } { 32 } , 0 \right) ;$ Directrix: $x = - \frac { 1 } { 32 } ;$ Focal width: $0.13$

Question 13

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola.
-$$4 x ^ { 2 } - 2 y ^ { 2 } + 2 x + 8 y + 2 = 0$$

Accepted Answer

A)  Parabola 
B)  Ellipse 
C)  Hyperbola 
A)  Parabola 
B)  Ellipse 
C)  Hyperbola

Question 14

Find an equation in standard form for the hyperbola that satisfies the given conditions.
-Foci at $( 0 , \pm 10 )$, a conjugate axis with length 8

Accepted Answer

A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ 
B)  $\frac { y ^ { 2 } } { 84 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 64 } = 1$ 
D)  $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 100 } = 1$ 
A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ 
B)  $\frac { y ^ { 2 } } { 84 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 64 } = 1$ 
D)  $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 100 } = 1$

Question 15

Find the standard form of the equation of the parabola.
-Vertex at $( - 7 , - 2 )$, opens to the left, focal width $= 14$

Accepted Answer

A)  $( y + 2 ) ^ { 2 } = - 14 ( x + 7 )$ 
B)  $( y + 2 ) ^ { 2 } = 14 ( x + 7 )$ 
C)  $( y + 2 ) ^ { 2 } = - 3.5 ( x + 7 )$ 
D)  $( x + 7 ) ^ { 2 } = 14 ( y + 2 )$ 
A)  $( y + 2 ) ^ { 2 } = - 14 ( x + 7 )$ 
B)  $( y + 2 ) ^ { 2 } = 14 ( x + 7 )$ 
C)  $( y + 2 ) ^ { 2 } = - 3.5 ( x + 7 )$ 
D)  $( x + 7 ) ^ { 2 } = 14 ( y + 2 )$

Question 16

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

Accepted Answer

A)  Vertex: $( 0,0 )$; Focus: $( 3,0 )$; Directrix: $x = - 3$; Focal width: 3 
B)  Vertex: $( 0,0 )$; Focus: $( - 3,0 )$; Directrix: $y = 3$; Focal wid th: 48 
C)  Vertex: $( 0,0 )$; Focus: $( 0 , - 3 )$; Directrix: $y = 3$; Focal width: 48 
D)  Vertex: $( 0,0 )$; Focus: $( - 3,0 )$; Directrix: $x = 3$; Focal width: 12 
A)  Vertex: $( 0,0 )$; Focus: $( 3,0 )$; Directrix: $x = - 3$; Focal width: 3 
B)  Vertex: $( 0,0 )$; Focus: $( - 3,0 )$; Directrix: $y = 3$; Focal wid th: 48 
C)  Vertex: $( 0,0 )$; Focus: $( 0 , - 3 )$; Directrix: $y = 3$; Focal width: 48 
D)  Vertex: $( 0,0 )$; Focus: $( - 3,0 )$; Directrix: $x = 3$; Focal width: 12

Question 17

Solve the problem.
-A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If $5 \mathrm {~m}$ down from the top of the dome the ceiling is $23 \mathrm {~m}$ wide, find the best location for the light source.

Accepted Answer

A)  $26.5 \mathrm {~m}$ down from the top 
B)  $19.8 \mathrm {~m}$ down from the top 
C)  $13.2 \mathrm {~m}$ down from the top 
D)  $6.6 \mathrm {~m}$ down from the top 
A)  $26.5 \mathrm {~m}$ down from the top 
B)  $19.8 \mathrm {~m}$ down from the top 
C)  $13.2 \mathrm {~m}$ down from the top 
D)  $6.6 \mathrm {~m}$ down from the top

Question 18

Graph the parabola.
-$$- 8 x = y ^ { 2 }$$

Accepted Answer

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

Question 19

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic.
-Directrix $y = - 9$, eccentricity 3

Accepted Answer

A)  $r = \frac { 9 } { 1 + 3 \sin \theta }$, hyperbola 
B)  $r = \frac { 3 } { 1 - 9 \sin \theta }$, hyperbola 
C)  $r = \frac { 27 } { 1 - 3 \sin \theta }$, hyperbola 
D)  $r = \frac { 9 } { 9 - \sin \theta }$, ellipse 
A)  $r = \frac { 9 } { 1 + 3 \sin \theta }$, hyperbola 
B)  $r = \frac { 3 } { 1 - 9 \sin \theta }$, hyperbola 
C)  $r = \frac { 27 } { 1 - 3 \sin \theta }$, hyperbola 
D)  $r = \frac { 9 } { 9 - \sin \theta }$, ellipse

Question 20

Graph the hyperbola.
-$$\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$$

Accepted Answer

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

Write an equation for the illustrated plane. -

Graph the ellipse. - $\frac{(x+2)^{2}}{16}+\frac{(y-3)^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+2)^{2}}{16}+\frac{(y-3)^{2}}{4}=1$

Write an equation for the sphere with the given point as its center and the given number as its radius. - $( 9,4,5 ) , 6$

Graph the parabola. - $8 y=-x^{2}$ $Graph the parabola. - 8 y=-x^{2}$

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - $3 x ^ { 2 } + 6 x y + 3 y ^ { 2 } - 2 x + 4 y = 0$

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with center at origin, length of major axis 14 and $y$ -intercepts $( 0 , \pm 6 )$

Find the vertex, focus, directrix, and focal width of the parabola. - $( x - 9 ) ^ { 2 } = - 8 ( y + 6 )$

Find an equation in standard form for the ellipse that satisfies the given conditions. -The vertical major axis is of length 8 , and the minor axis is of length 4 .

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic. -Directrix $x = - 8$ , eccentricity 3

Find the vertex, focus, directrix, and focal width of the parabola. - $x = 8 y ^ { 2 }$

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - $4 x ^ { 2 } - 2 y ^ { 2 } + 2 x + 8 y + 2 = 0$

Find an equation in standard form for the hyperbola that satisfies the given conditions. -Foci at $( 0 , \pm 10 )$ , a conjugate axis with length 8

Find the standard form of the equation of the parabola. -Vertex at $( - 7 , - 2 )$ , opens to the left, focal width $= 14$

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

Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If $5 \mathrm {~m}$ down from the top of the dome the ceiling is $23 \mathrm {~m}$ wide, find the best location for the light source.

Graph the parabola. - $- 8 x = y ^ { 2 }$ $Graph the parabola. - - 8 x = y ^ { 2 }$

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic. -Directrix $y = - 9$ , eccentricity 3

Graph the hyperbola. - $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 8: Analytic Geometry in Two and Three Dimensions

Write an equation for the illustrated plane. -

Graph the ellipse. - (x+2)216+(y−3)24=1\frac{(x+2)^{2}}{16}+\frac{(y-3)^{2}}{4}=116(x+2)2​+4(y−3)2​=1

Write an equation for the sphere with the given point as its center and the given number as its radius. - (9,4,5),6( 9,4,5 ) , 6(9,4,5),6

Graph the parabola. - 8y=−x28 y=-x^{2}8y=−x2

Solve the problem. - A radio telescope has a parabolic surface. If it is 9 m9 \mathrm {~m}9 m deep and 12 m12 \mathrm {~m}12 m wide, how far is the focus from the vertex?

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - 3x2+6xy+3y2−2x+4y=03 x ^ { 2 } + 6 x y + 3 y ^ { 2 } - 2 x + 4 y = 03x2+6xy+3y2−2x+4y=0

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with center at origin, length of major axis 14 and yyy -intercepts (0,±6)( 0 , \pm 6 )(0,±6)

Solve the problem. - A building has an entry the shape of a parabolic arch 98ft98 \mathrm { ft }98ft high and 30ft30 \mathrm { ft }30ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Find the vertex, focus, directrix, and focal width of the parabola. - (x−9)2=−8(y+6)( x - 9 ) ^ { 2 } = - 8 ( y + 6 )(x−9)2=−8(y+6)

Find an equation in standard form for the ellipse that satisfies the given conditions. -The vertical major axis is of length 8 , and the minor axis is of length 4 .

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic. -Directrix x=−8x = - 8x=−8 , eccentricity 3

Find the vertex, focus, directrix, and focal width of the parabola. - x=8y2x = 8 y ^ { 2 }x=8y2

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - 4x2−2y2+2x+8y+2=04 x ^ { 2 } - 2 y ^ { 2 } + 2 x + 8 y + 2 = 04x2−2y2+2x+8y+2=0

Find an equation in standard form for the hyperbola that satisfies the given conditions. -Foci at (0,±10)( 0 , \pm 10 )(0,±10) , a conjugate axis with length 8

Find the standard form of the equation of the parabola. -Vertex at (−7,−2)( - 7 , - 2 )(−7,−2) , opens to the left, focal width =14= 14=14

Find the vertex, focus, directrix, and focal width of the parabola. - y2=−12xy ^ { 2 } = - 12 xy2=−12x

Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 5 m5 \mathrm {~m}5 m down from the top of the dome the ceiling is 23 m23 \mathrm {~m}23 m wide, find the best location for the light source.

Graph the parabola. - −8x=y2- 8 x = y ^ { 2 }−8x=y2

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic. -Directrix y=−9y = - 9y=−9 , eccentricity 3

Graph the hyperbola. - x264−y24=1\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 164x2​−4y2​=1

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Graph the ellipse. - $\frac{(x+2)^{2}}{16}+\frac{(y-3)^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+2)^{2}}{16}+\frac{(y-3)^{2}}{4}=1$

Write an equation for the sphere with the given point as its center and the given number as its radius. - $( 9,4,5 ) , 6$

Graph the parabola. - $8 y=-x^{2}$ $Graph the parabola. - 8 y=-x^{2}$

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - $3 x ^ { 2 } + 6 x y + 3 y ^ { 2 } - 2 x + 4 y = 0$

Find an equation in standard form for the ellipse that satisfies the given conditions. -An ellipse with center at origin, length of major axis 14 and $y$ -intercepts $( 0 , \pm 6 )$

Find the vertex, focus, directrix, and focal width of the parabola. - $( x - 9 ) ^ { 2 } = - 8 ( y + 6 )$

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic. -Directrix $x = - 8$ , eccentricity 3

Find the vertex, focus, directrix, and focal width of the parabola. - $x = 8 y ^ { 2 }$

Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. - $4 x ^ { 2 } - 2 y ^ { 2 } + 2 x + 8 y + 2 = 0$

Find an equation in standard form for the hyperbola that satisfies the given conditions. -Foci at $( 0 , \pm 10 )$ , a conjugate axis with length 8

Find the standard form of the equation of the parabola. -Vertex at $( - 7 , - 2 )$ , opens to the left, focal width $= 14$

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

Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If $5 \mathrm {~m}$ down from the top of the dome the ceiling is $23 \mathrm {~m}$ wide, find the best location for the light source.

Graph the parabola. - $- 8 x = y ^ { 2 }$ $Graph the parabola. - - 8 x = y ^ { 2 }$

Find the polar equation of the conic with focus at the pole, having the given properties. Identify the conic. -Directrix $y = - 9$ , eccentricity 3

Graph the hyperbola. - $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$