Question 1

Write an equation for the parabola.
-vertex: $( - 4,3 )$, directrix: $x = - 6$

Accepted Answer

A)  $( y - 3 ) ^ { 2 } = 8 ( x + 4 )$ 
B)  $( x - 3 ) ^ { 2 } = 8 ( y + 4 )$ 
C)  $( x + 4 ) ^ { 2 } = - 8 ( x - 3 )$ 
D)  $( y - 3 ) ^ { 2 } = - 8 ( x + 4 )$ 
A)  $( y - 3 ) ^ { 2 } = 8 ( x + 4 )$ 
B)  $( x - 3 ) ^ { 2 } = 8 ( y + 4 )$ 
C)  $( x + 4 ) ^ { 2 } = - 8 ( x - 3 )$ 
D)  $( y - 3 ) ^ { 2 } = - 8 ( x + 4 )$

Question 2

Graph the conic section.
-$$y ^ { 2 } - 12 y + 4 x + 48 = 0$$

Accepted Answer

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

Question 3

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 81 } = 1$$

Accepted Answer

A)  $y = \frac { 9 \sqrt { 5184 - 4 x ^ { 2 } } } { 16 }$ and $y = - \frac { 9 \sqrt { 5184 - 4 x ^ { 2 } } } { 16 }$ 
B)  $y = \frac { 16 - 9 \sqrt { 64 - x ^ { 2 } } } { 8 }$ and $y = \frac { 9 \sqrt { 64 - x ^ { 2 } } + 16 } { 8 }$ 
C)  $y = \frac { \sqrt { 5440 - 81 x ^ { 2 } } } { 8 }$ and $y = - \frac { \sqrt { 5440 - 81 x ^ { 2 } } } { 8 }$ 
D)  $y = \frac { \sqrt { 256 - 81 x ^ { 2 } } } { 8 }$ and $y = - \frac { \sqrt { 256 - 81 x ^ { 2 } } } { 8 }$ 
A)  $y = \frac { 9 \sqrt { 5184 - 4 x ^ { 2 } } } { 16 }$ and $y = - \frac { 9 \sqrt { 5184 - 4 x ^ { 2 } } } { 16 }$ 
B)  $y = \frac { 16 - 9 \sqrt { 64 - x ^ { 2 } } } { 8 }$ and $y = \frac { 9 \sqrt { 64 - x ^ { 2 } } + 16 } { 8 }$ 
C)  $y = \frac { \sqrt { 5440 - 81 x ^ { 2 } } } { 8 }$ and $y = - \frac { \sqrt { 5440 - 81 x ^ { 2 } } } { 8 }$ 
D)  $y = \frac { \sqrt { 256 - 81 x ^ { 2 } } } { 8 }$ and $y = - \frac { \sqrt { 256 - 81 x ^ { 2 } } } { 8 }$

Question 4

Provide an appropriate response.
-The eccentricity of ellipse $\mathrm { A }$ is $\mathrm { e } _ { \mathrm { A } } = 0.18$ and the eccentricity of ellipse $\mathrm { B }$ is $\mathrm { eB } = 0.82$. Which ellipse is flatter?

Accepted Answer

The answer of Provide an appropriate response.
-The eccentricity of ellipse...

Question 5

Match the equation of the parabola with the appropriate description.
-$$y + 2 = 2 ( x + 15 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( - 15 , - 2 )$ 
B)  Vertex at $( 15 , - 2 )$ 
C)  Vertex at $( 2,15 )$ 
D)  Vertex at $( - 2,15 )$ 
A)  Vertex at $( - 15 , - 2 )$ 
B)  Vertex at $( 15 , - 2 )$ 
C)  Vertex at $( 2,15 )$ 
D)  Vertex at $( - 2,15 )$

Question 6

Graph the equation. Give the domain and range. Identify whether the equation is a function.
-$$\frac { y } { 9 } = \sqrt { 1 - \frac { x ^ { 2 } } { 49 } }$$

Accepted Answer

A) 
 
$[-7,7] ;[0,1] ; \text { not a function }$ 
B) 
 
$[-7,7] ;[0,9] ; \text { function }$ 
C) 
 
$[ - 7,7 ] ; [ - 1,0 ] ;$ not a function 
D) 
 
$[ - 7,7 ] ; [ - 9,0 ]$; function

Question 7

Find the eccentricity of the conic section shown in the graph.
-If a satellite is scheduled to leave Earth's gravitational influence, its velocity must be increased so that its trajectory changes from elliptical to hyperbolic. Determine the minimum increase in
Velocity necessary for a satellite traveling at a velocity of 5698 meters per second to escape Earth's
Gravitational influence when $$D = 142 \times 10 ^ { 6 }$$ m.

Accepted Answer

A)  5773 m per sec 
B)  8064 m per sec 
C)  5623 m per sec 
D)  -3332 m per sec 
A)  5773 m per sec 
B)  8064 m per sec 
C)  5623 m per sec 
D)  -3332 m per sec

Question 8

Write an equation for the hyperbola.
-The roof of a building is in the shape of the hyperbola $y ^ { 2 } - 2 x ^ { 2 } = 56$, where $x$ and $y$ are in meters. Refer to the figure and determine the height, $h$, of the outside walls.
$$A = 3 \mathrm {~m}$$

Accepted Answer

A)  $3.3 \mathrm {~m}$ 
B)  $11 \mathrm {~m}$ 
C)  $8.6 \mathrm {~m}$ 
D)  $74 \mathrm {~m}$ 
A)  $3.3 \mathrm {~m}$ 
B)  $11 \mathrm {~m}$ 
C)  $8.6 \mathrm {~m}$ 
D)  $74 \mathrm {~m}$

Question 9

Provide an appropriate response.
-Suppose that $A C > 0$ and $A \neq C$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$. What kind of graph does this equation have?

Accepted Answer

The equati

Question 10

Graph the parabola.
-$x=(y-3)^{2}$

Accepted Answer

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

Question 11

Find the eccentricity e of the ellipse.
-An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4
Sides

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 6 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 100 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 6 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 100 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 9 } = 1$

Question 12

Graph the conic section.
-$$9 x ^ { 2 } - 16 y ^ { 2 } - 36 x - 96 y - 252 = 0$$

Accepted Answer

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

Question 13

Find the center, foci, and asymptotes of the hyperbola.
-$$x ^ { 2 } - y ^ { 2 } = 32$$

Accepted Answer

A)  C: $( 2,2 ) ; F : ( 8,0 ) , ( - 8,0 ) ; A : y = 2 x , y = - 2 x$ 
B)  $C : ( 0,0 ) ; F : ( 4,0 ) , ( - 4,0 ) ; A : y = x , y = - x$ 
C)  C: $( 0,0 ) ; F : ( 8,0 ) , ( - 8,0 ) ; A : y = x , y = - x$ 
D)  C: $( 0,0 ) ; F : ( 8,0 ) , ( - 8,0 ) ; A : y = 2 x , y = - 2 x$ 
A)  C: $( 2,2 ) ; F : ( 8,0 ) , ( - 8,0 ) ; A : y = 2 x , y = - 2 x$ 
B)  $C : ( 0,0 ) ; F : ( 4,0 ) , ( - 4,0 ) ; A : y = x , y = - x$ 
C)  C: $( 0,0 ) ; F : ( 8,0 ) , ( - 8,0 ) ; A : y = x , y = - x$ 
D)  C: $( 0,0 ) ; F : ( 8,0 ) , ( - 8,0 ) ; A : y = 2 x , y = - 2 x$

Question 14

Match the equation of the parabola with the appropriate description.
-$y = 6 x ^ { 2 } - 6 x + 4$

Accepted Answer

A)  Opens left 
B)  Opens up 
C)  Opens down 
D)  Opens right 
A)  Opens left 
B)  Opens up 
C)  Opens down 
D)  Opens right

Question 15

Write an equation for the hyperbola.
-vertices at $( 0,3 ) , ( 0 , - 3 )$; foci at $( 0,7 ) , ( 0 , - 7 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 9 } = 1$ 
B)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 1$ 
D)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$ 
A)  $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 9 } = 1$ 
B)  $\frac { y ^ { 2 } } { 40 } - \frac { x ^ { 2 } } { 9 } = 1$ 
C)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 49 } = 1$ 
D)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 40 } = 1$

Question 16

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$4 x ^ { 2 } + 16 y ^ { 2 } = 64$

Accepted Answer

A)  Hyperbola 
B)  Parabola 
C)  Ellipse 
D)  Circle 
A)  Hyperbola 
B)  Parabola 
C)  Ellipse 
D)  Circle

Question 17

Write an equation for the hyperbola.
-A nuclear cooling tower cross section is a hyperbola having a diameter of $60 \mathrm { ft }$ at the center. The distance between the two foci is $92 \mathrm { ft }$. What is the equation for the hyperbola?

Accepted Answer

A)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 5$ 
B)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1218 } = 1$ 
C)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 2116 } = 1$ 
D)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 1$ 
A)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 5$ 
B)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1218 } = 1$ 
C)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 2116 } = 1$ 
D)  $\frac { x ^ { 2 } } { 900 } - \frac { y ^ { 2 } } { 1216 } = 1$

Question 18

Match the equation of the parabola with the appropriate description.
-$$x + 2 = 2 ( y + 7 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( - 7 , - 2 )$ 
B)  Vertex at $( 2,7 )$ 
C)  Vertex at $( - 2 , - 7 )$ 
D)  Vertex at $( 7,2 )$ 
A)  Vertex at $( - 7 , - 2 )$ 
B)  Vertex at $( 2,7 )$ 
C)  Vertex at $( - 2 , - 7 )$ 
D)  Vertex at $( 7,2 )$

Question 19

Find the eccentricity of the conic section shown in the graph.
-X = - 1/2

Accepted Answer

A)  $e = 3$ 
B)  $e = 1$ 
C)  $e = 2$ 
D)  $e = \frac { 1 } { 2 }$ 
A)  $e = 3$ 
B)  $e = 1$ 
C)  $e = 2$ 
D)  $e = \frac { 1 } { 2 }$

Question 20

Write an equation for the ellipse.
-foci at $( \pm 4 \sqrt { 2 } , 0 ) ; x$-intercepts $( \pm 9,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 7 } = 1$ 
C)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = 1$ 
A)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 7 } = 1$ 
C)  $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = 1$

Write an equation for the parabola. -vertex: $( - 4,3 )$ , directrix: $x = - 6$

Graph the conic section. - $y ^ { 2 } - 12 y + 4 x + 48 = 0$ $Graph the conic section. - y ^ { 2 } - 12 y + 4 x + 48 = 0$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 81 } = 1$

Provide an appropriate response. -The eccentricity of ellipse $\mathrm { A }$ is $\mathrm { e } _ { \mathrm { A } } = 0.18$ and the eccentricity of ellipse $\mathrm { B }$ is $\mathrm { eB } = 0.82$ . Which ellipse is flatter?

Match the equation of the parabola with the appropriate description. - $y + 2 = 2 ( x + 15 ) ^ { 2 }$

Provide an appropriate response. -Suppose that $A C > 0$ and $A \neq C$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$ . What kind of graph does this equation have?

Graph the parabola. - $x=(y-3)^{2}$ $Graph the parabola. - x=(y-3)^{2}$

Find the eccentricity e of the ellipse. -An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 Sides

Graph the conic section. - $9 x ^ { 2 } - 16 y ^ { 2 } - 36 x - 96 y - 252 = 0$ $Graph the conic section. - 9 x ^ { 2 } - 16 y ^ { 2 } - 36 x - 96 y - 252 = 0$

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 32$

Match the equation of the parabola with the appropriate description. - $y = 6 x ^ { 2 } - 6 x + 4$

Write an equation for the hyperbola. -vertices at $( 0,3 ) , ( 0 , - 3 )$ ; foci at $( 0,7 ) , ( 0 , - 7 )$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } + 16 y ^ { 2 } = 64$

Write an equation for the hyperbola. -A nuclear cooling tower cross section is a hyperbola having a diameter of $60 \mathrm { ft }$ at the center. The distance between the two foci is $92 \mathrm { ft }$ . What is the equation for the hyperbola?

Match the equation of the parabola with the appropriate description. - $x + 2 = 2 ( y + 7 ) ^ { 2 }$

Find the eccentricity of the conic section shown in the graph. -X = - 1/2

Write an equation for the ellipse. -foci at $( \pm 4 \sqrt { 2 } , 0 ) ; x$ -intercepts $( \pm 9,0 )$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Further Topics in Algebra

Filters

Exam 11: Analytic Geometry

Write an equation for the parabola. -vertex: (−4,3)( - 4,3 )(−4,3) , directrix: x=−6x = - 6x=−6

Graph the conic section. - y2−12y+4x+48=0y ^ { 2 } - 12 y + 4 x + 48 = 0y2−12y+4x+48=0

Determine the two equations necessary to graph the ellipse with a graphing calculator. - x264+(y−2)281=1\frac { x ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 81 } = 164x2​+81(y−2)2​=1

Provide an appropriate response. -The eccentricity of ellipse A\mathrm { A }A is eA=0.18\mathrm { e } _ { \mathrm { A } } = 0.18eA​=0.18 and the eccentricity of ellipse B\mathrm { B }B is eB=0.82\mathrm { eB } = 0.82eB=0.82 . Which ellipse is flatter?

Match the equation of the parabola with the appropriate description. - y+2=2(x+15)2y + 2 = 2 ( x + 15 ) ^ { 2 }y+2=2(x+15)2

Graph the equation. Give the domain and range. Identify whether the equation is a function. - y9=1−x249\frac { y } { 9 } = \sqrt { 1 - \frac { x ^ { 2 } } { 49 } }9y​=1−49x2​​

Write an equation for the hyperbola. -The roof of a building is in the shape of the hyperbola y2−2x2=56y ^ { 2 } - 2 x ^ { 2 } = 56y2−2x2=56 , where xxx and yyy are in meters. Refer to the figure and determine the height, hhh , of the outside walls. A=3 mA = 3 \mathrm {~m}A=3 m

Provide an appropriate response. -Suppose that AC>0A C > 0AC>0 and A≠CA \neq CA=C in the equation Ax2+Bx+Cy2+Dy+E=0A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0Ax2+Bx+Cy2+Dy+E=0 . What kind of graph does this equation have?

Graph the parabola. - x=(y−3)2x=(y-3)^{2}x=(y−3)2

Find the eccentricity e of the ellipse. -An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 Sides

Graph the conic section. - 9x2−16y2−36x−96y−252=09 x ^ { 2 } - 16 y ^ { 2 } - 36 x - 96 y - 252 = 09x2−16y2−36x−96y−252=0

Find the center, foci, and asymptotes of the hyperbola. - x2−y2=32x ^ { 2 } - y ^ { 2 } = 32x2−y2=32

Match the equation of the parabola with the appropriate description. - y=6x2−6x+4y = 6 x ^ { 2 } - 6 x + 4y=6x2−6x+4

Write an equation for the hyperbola. -vertices at (0,3),(0,−3)( 0,3 ) , ( 0 , - 3 )(0,3),(0,−3) ; foci at (0,7),(0,−7)( 0,7 ) , ( 0 , - 7 )(0,7),(0,−7)

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 4x2+16y2=644 x ^ { 2 } + 16 y ^ { 2 } = 644x2+16y2=64

Write an equation for the hyperbola. -A nuclear cooling tower cross section is a hyperbola having a diameter of 60ft60 \mathrm { ft }60ft at the center. The distance between the two foci is 92ft92 \mathrm { ft }92ft . What is the equation for the hyperbola?

Match the equation of the parabola with the appropriate description. - x+2=2(y+7)2x + 2 = 2 ( y + 7 ) ^ { 2 }x+2=2(y+7)2

Find the eccentricity of the conic section shown in the graph. -X = - 1/2

Write an equation for the ellipse. -foci at (±42,0);x( \pm 4 \sqrt { 2 } , 0 ) ; x(±42​,0);x -intercepts (±9,0)( \pm 9,0 )(±9,0)

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Further Topics in Algebra

Filters

Write an equation for the parabola. -vertex: $( - 4,3 )$ , directrix: $x = - 6$

Graph the conic section. - $y ^ { 2 } - 12 y + 4 x + 48 = 0$ $Graph the conic section. - y ^ { 2 } - 12 y + 4 x + 48 = 0$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 81 } = 1$

Provide an appropriate response. -The eccentricity of ellipse $\mathrm { A }$ is $\mathrm { e } _ { \mathrm { A } } = 0.18$ and the eccentricity of ellipse $\mathrm { B }$ is $\mathrm { eB } = 0.82$ . Which ellipse is flatter?

Match the equation of the parabola with the appropriate description. - $y + 2 = 2 ( x + 15 ) ^ { 2 }$

Provide an appropriate response. -Suppose that $A C > 0$ and $A \neq C$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$ . What kind of graph does this equation have?

Graph the parabola. - $x=(y-3)^{2}$ $Graph the parabola. - x=(y-3)^{2}$

Graph the conic section. - $9 x ^ { 2 } - 16 y ^ { 2 } - 36 x - 96 y - 252 = 0$ $Graph the conic section. - 9 x ^ { 2 } - 16 y ^ { 2 } - 36 x - 96 y - 252 = 0$

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 32$

Match the equation of the parabola with the appropriate description. - $y = 6 x ^ { 2 } - 6 x + 4$

Write an equation for the hyperbola. -vertices at $( 0,3 ) , ( 0 , - 3 )$ ; foci at $( 0,7 ) , ( 0 , - 7 )$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } + 16 y ^ { 2 } = 64$

Write an equation for the hyperbola. -A nuclear cooling tower cross section is a hyperbola having a diameter of $60 \mathrm { ft }$ at the center. The distance between the two foci is $92 \mathrm { ft }$ . What is the equation for the hyperbola?

Match the equation of the parabola with the appropriate description. - $x + 2 = 2 ( y + 7 ) ^ { 2 }$

Write an equation for the ellipse. -foci at $( \pm 4 \sqrt { 2 } , 0 ) ; x$ -intercepts $( \pm 9,0 )$