Question 1

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$x + 3 = ( y + 7 ) ^ { 2 }$

Accepted Answer

A)  $y = \sqrt { x - 4 }$ and $y = - \sqrt { x - 4 }$ 
B)  $y = \sqrt { x + 3 } - 7$ and $y = - \sqrt { x + 3 } - 7$ 
C)  $y = \sqrt { x + 10 }$ and $y = - \sqrt { x + 10 }$ 
D)  $y = \sqrt { x + 3 } - 7$ and $y = - \sqrt { x + 3 } + 7$ 
A)  $y = \sqrt { x - 4 }$ and $y = - \sqrt { x - 4 }$ 
B)  $y = \sqrt { x + 3 } - 7$ and $y = - \sqrt { x + 3 } - 7$ 
C)  $y = \sqrt { x + 10 }$ and $y = - \sqrt { x + 10 }$ 
D)  $y = \sqrt { x + 3 } - 7$ and $y = - \sqrt { x + 3 } + 7$

Question 2

Graph the parabola.
-

Accepted Answer

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

Question 3

Find the eccentricity of the ellipse.
-$$x ^ { 2 } + 2 y ^ { 2 } = 6$$

Accepted Answer

A)  $\sqrt { 2 }$ 
B)  $\sqrt { 6 }$ 
C)  $\frac { \sqrt { 6 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$ 
A)  $\sqrt { 2 }$ 
B)  $\sqrt { 6 }$ 
C)  $\frac { \sqrt { 6 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$

Question 4

Write the word or phrase that best completes each statement or answers the question.
-It can be shown that a hyperbola with center at the origin, foci at $\mathrm { F } ^ { \prime } ( - \mathrm { c } , 0 )$ and $\mathrm { F } ( \mathrm { c } , 0 )$, and equation $d \left( P , F ^ { \prime } \right) - d ( P , F ) = 2 a$ has equation $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$. Use this result to find an equation of a hyperbola with center at the origin, foci at $( - 6,0 )$ and $( 6,0 )$, and absolute value of the distances from any point of the hyperbola to the two foci equal to 6 .

Accepted Answer

A)  $x ^ { 2 } - y ^ { 2 } = 6$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 45 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 6 } = 1$ 
A)  $x ^ { 2 } - y ^ { 2 } = 6$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 27 } = 1$ 
C)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 45 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 6 } = 1$

Question 5

Find the eccentricity of the hyperbola.
-$$x ^ { 2 } - 2 y ^ { 2 } = 6$$

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  $\sqrt { 6 }$ 
D)  $\frac { \sqrt { 6 } } { 2 }$ 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  $\sqrt { 6 }$ 
D)  $\frac { \sqrt { 6 } } { 2 }$

Question 6

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { ( x - 6 ) ^ { 2 } } { 4 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( y - 2 ) ^ { 2 } } { 9 } - \frac { ( x - 6 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x - 6 ) ^ { 2 } } { 4 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$ 
A)  $\frac { ( x - 6 ) ^ { 2 } } { 4 } - \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x - 6 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( y - 2 ) ^ { 2 } } { 9 } - \frac { ( x - 6 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( x - 6 ) ^ { 2 } } { 4 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$

Question 7

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( - 3,0 )$ is one-fourth of the distance from the line $x = - 11$.

Accepted Answer

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

Question 8

Write the word or phrase that best completes each statement or answers the question.
-$$\frac { 25 x ^ { 2 } } { 36 } + 4 y ^ { 2 } = 1600$$

Accepted Answer

A)  $x$-intercepts $\pm 20 ; y$-intercepts $\pm 48$ 
B)  $x$-intercepts $\pm \frac { 20 } { 3 } ; y$-intercepts $\pm 40$ 
C)  $x$-intercepts $\pm 48 ; y$-intercepts $\pm 20$ 
D)  $x$-intercepts $\pm 2304 ; y$-intercepts $\pm 41$ 
A)  $x$-intercepts $\pm 20 ; y$-intercepts $\pm 48$ 
B)  $x$-intercepts $\pm \frac { 20 } { 3 } ; y$-intercepts $\pm 40$ 
C)  $x$-intercepts $\pm 48 ; y$-intercepts $\pm 20$ 
D)  $x$-intercepts $\pm 2304 ; y$-intercepts $\pm 41$

Question 9

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 36 } = 1$$

Accepted Answer

A)  $x = \frac { 5 \sqrt { 25 - y ^ { 2 } } } { 36 }$ and $x = - \frac { 5 \sqrt { 25 - y ^ { 2 } } } { 36 }$ 
B)  $y = \frac { 6 \sqrt { 25 - x ^ { 2 } } } { 5 }$ and $y = - \frac { 6 \sqrt { 25 - x ^ { 2 } } } { 5 }$ 
C)  $x = \sqrt { \frac { 180 - x ^ { 2 } } { 6 } }$ and $x = - \sqrt { \frac { 180 - y ^ { 2 } } { 6 } }$ 
D)  $y = \frac { 6 \sqrt { 25 - x ^ { 2 } } } { 25 }$ and $y = - \frac { 6 \sqrt { 25 + x ^ { 2 } } } { 25 }$ 
A)  $x = \frac { 5 \sqrt { 25 - y ^ { 2 } } } { 36 }$ and $x = - \frac { 5 \sqrt { 25 - y ^ { 2 } } } { 36 }$ 
B)  $y = \frac { 6 \sqrt { 25 - x ^ { 2 } } } { 5 }$ and $y = - \frac { 6 \sqrt { 25 - x ^ { 2 } } } { 5 }$ 
C)  $x = \sqrt { \frac { 180 - x ^ { 2 } } { 6 } }$ and $x = - \sqrt { \frac { 180 - y ^ { 2 } } { 6 } }$ 
D)  $y = \frac { 6 \sqrt { 25 - x ^ { 2 } } } { 25 }$ and $y = - \frac { 6 \sqrt { 25 + x ^ { 2 } } } { 25 }$

Question 10

Graph the hyperbola.
-$$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 36 } = 1$$

Accepted Answer

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

Question 11

Give the focus, directrix, and axis for the parabola.
-$$x ^ { 2 } = 12 y$$

Accepted Answer

A)  $( 0 , - 3 ) , x = - 3 , x$-axis 
B)  $( 0,3 ) , y = - 3 , y$-axis 
C)  $( 3,0 ) , x = 3 , x$-axis 
D)  $( 3,0 ) , y = 3$, y-axis 
A)  $( 0 , - 3 ) , x = - 3 , x$-axis 
B)  $( 0,3 ) , y = - 3 , y$-axis 
C)  $( 3,0 ) , x = 3 , x$-axis 
D)  $( 3,0 ) , y = 3$, y-axis

Question 12

When a satellite is near Earth, its orbital trajectory may trace out a hyperbola, a parabola, or an ellipse. The type of trajectory depends on the satellite's velocity $V$ in meters per second. It will be hyperbolic if $V > \frac { k } { \sqrt { D } }$, parabolic if $V =$ $\frac { k } { \sqrt { D } }$, and elliptical if $V < \frac { k } { \sqrt { D } }$, where $k = 2.82 \times 10 ^ { 7 }$ is a constant and $\mathrm { D }$ is the distance in meters from the satellite to the center of Earth. Solve the problem.
-When a certain satellite was at a maximum distance of 61.7 × 106 m from Earthʹs center, it had a velocity of 5668 m per sec. Determine the shape of its trajectory.

Accepted Answer

A)  parabolic 
B)  hyperbolic 
C)  elliptical 
A)  parabolic 
B)  hyperbolic 
C)  elliptical

Question 13

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$( x - 6 ) ^ { 2 } = 36 - y ^ { 2 }$$

Accepted Answer

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

Question 14

Write an equation for the ellipse.
-$\mathrm { x }$-intercepts $\pm 6 ; \mathrm { y }$-intercepts $\pm 8$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 8 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 8 } = 1$ 
B)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 64 } = 1$

Question 15

Write an equation for the hyperbola.
-$x$-intercept 4 ; center at origin; passing through $( 4 \sqrt { 5 } , 6 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$

Question 16

Solve the problem.
-A rectangular board is 2 feet by 18 feet. How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

Accepted Answer

A)  8.9 ft 
B)  8.0 ft 
C)  1.0 ft 
D)  0.1 ft 
A)  8.9 ft 
B)  8.0 ft 
C)  1.0 ft 
D)  0.1 ft

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

A)  Vertex at $( - 6 , - 4 )$ 
B)  Vertex at $( 12,4 )$ 
C)  Vertex at $( 6,4 )$ 
D)  Vertex at $( - 12 , - 4 )$ 
A)  Vertex at $( - 6 , - 4 )$ 
B)  Vertex at $( 12,4 )$ 
C)  Vertex at $( 6,4 )$ 
D)  Vertex at $( - 12 , - 4 )$

Question 19

Write an equation for the hyperbola.
-vertices $( - 6 , - 2 ) , ( - 6,16 )$; eccentricity $\frac { \sqrt { 106 } } { 9 }$

Accepted Answer

A)  $\frac { ( y - 6 ) ^ { 2 } } { 81 } - \frac { ( x + 7 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( y - 7 ) ^ { 2 } } { 81 } - \frac { ( x + 6 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( y - 6 ) ^ { 2 } } { 81 } - \frac { ( x - 7 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( y + 6 ) ^ { 2 } } { 25 } - \frac { ( x - 7 ) ^ { 2 } } { 81 } = 1$ 
A)  $\frac { ( y - 6 ) ^ { 2 } } { 81 } - \frac { ( x + 7 ) ^ { 2 } } { 25 } = 1$ 
B)  $\frac { ( y - 7 ) ^ { 2 } } { 81 } - \frac { ( x + 6 ) ^ { 2 } } { 25 } = 1$ 
C)  $\frac { ( y - 6 ) ^ { 2 } } { 81 } - \frac { ( x - 7 ) ^ { 2 } } { 25 } = 1$ 
D)  $\frac { ( y + 6 ) ^ { 2 } } { 25 } - \frac { ( x - 7 ) ^ { 2 } } { 81 } = 1$

Question 20

Write the word or phrase that best completes each statement or answers the question.
-There are some fundamental differences between graphing a hyperbola centered at the
origin and graphing an ellipse centered at the origin. What are these differences?

Accepted Answer

Answers will vary. One possibility: To g

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x + 3 = ( y + 7 ) ^ { 2 }$

Graph the parabola. -

Find the eccentricity of the ellipse. - $x ^ { 2 } + 2 y ^ { 2 } = 6$

Find the eccentricity of the hyperbola. - $x ^ { 2 } - 2 y ^ { 2 } = 6$

Choose the equation that matches the graph. -

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( - 3,0 )$ is one-fourth of the distance from the line $x = - 11$ .

Write the word or phrase that best completes each statement or answers the question. - $\frac { 25 x ^ { 2 } } { 36 } + 4 y ^ { 2 } = 1600$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 36 } = 1$

Graph the hyperbola. - $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 36 } = 1$

Give the focus, directrix, and axis for the parabola. - $x ^ { 2 } = 12 y$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $( x - 6 ) ^ { 2 } = 36 - y ^ { 2 }$

Write an equation for the ellipse. - $\mathrm { x }$ -intercepts $\pm 6 ; \mathrm { y }$ -intercepts $\pm 8$

Write an equation for the hyperbola. - $x$ -intercept 4 ; center at origin; passing through $( 4 \sqrt { 5 } , 6 )$

Solve the problem. -A rectangular board is 2 feet by 18 feet. How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

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

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

Write an equation for the hyperbola. -vertices $( - 6 , - 2 ) , ( - 6,16 )$ ; eccentricity $\frac { \sqrt { 106 } } { 9 }$

Write the word or phrase that best completes each statement or answers the question. -There are some fundamental differences between graphing a hyperbola centered at the origin and graphing an ellipse centered at the origin. What are these differences?

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Exam 10: Analytic Geometry

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x+3=(y+7)2x + 3 = ( y + 7 ) ^ { 2 }x+3=(y+7)2

Graph the parabola. -

Find the eccentricity of the ellipse. - x2+2y2=6x ^ { 2 } + 2 y ^ { 2 } = 6x2+2y2=6

Find the eccentricity of the hyperbola. - x2−2y2=6x ^ { 2 } - 2 y ^ { 2 } = 6x2−2y2=6

Choose the equation that matches the graph. -

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point (−3,0)( - 3,0 )(−3,0) is one-fourth of the distance from the line x=−11x = - 11x=−11 .

Write the word or phrase that best completes each statement or answers the question. - 25x236+4y2=1600\frac { 25 x ^ { 2 } } { 36 } + 4 y ^ { 2 } = 16003625x2​+4y2=1600

Determine the two equations necessary to graph the ellipse with a graphing calculator. - x225+y236=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 36 } = 125x2​+36y2​=1

Graph the hyperbola. - x24−y236=1\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 36 } = 14x2​−36y2​=1

Give the focus, directrix, and axis for the parabola. - x2=12yx ^ { 2 } = 12 yx2=12y

Identify the equation as a parabola, circle, ellipse, or hyperbola. - (x−6)2=36−y2( x - 6 ) ^ { 2 } = 36 - y ^ { 2 }(x−6)2=36−y2

Write an equation for the ellipse. - x\mathrm { x }x -intercepts ±6;y\pm 6 ; \mathrm { y }±6;y -intercepts ±8\pm 8±8

Write an equation for the hyperbola. - xxx -intercept 4 ; center at origin; passing through (45,6)( 4 \sqrt { 5 } , 6 )(45​,6)

Solve the problem. -A rectangular board is 2 feet by 18 feet. How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

Graph the hyperbola. - (x+1)24−(y−1)264=1\frac { ( x + 1 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 64 } = 14(x+1)2​−64(y−1)2​=1

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

Write an equation for the hyperbola. -vertices (−6,−2),(−6,16)( - 6 , - 2 ) , ( - 6,16 )(−6,−2),(−6,16) ; eccentricity 1069\frac { \sqrt { 106 } } { 9 }9106​​

Write the word or phrase that best completes each statement or answers the question. -There are some fundamental differences between graphing a hyperbola centered at the origin and graphing an ellipse centered at the origin. What are these differences?

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

Review of Basic Concepts

Filters

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x + 3 = ( y + 7 ) ^ { 2 }$

Find the eccentricity of the ellipse. - $x ^ { 2 } + 2 y ^ { 2 } = 6$

Find the eccentricity of the hyperbola. - $x ^ { 2 } - 2 y ^ { 2 } = 6$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the distance from the point $( - 3,0 )$ is one-fourth of the distance from the line $x = - 11$ .

Write the word or phrase that best completes each statement or answers the question. - $\frac { 25 x ^ { 2 } } { 36 } + 4 y ^ { 2 } = 1600$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 36 } = 1$

Graph the hyperbola. - $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 36 } = 1$

Give the focus, directrix, and axis for the parabola. - $x ^ { 2 } = 12 y$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $( x - 6 ) ^ { 2 } = 36 - y ^ { 2 }$

Write an equation for the ellipse. - $\mathrm { x }$ -intercepts $\pm 6 ; \mathrm { y }$ -intercepts $\pm 8$

Write an equation for the hyperbola. - $x$ -intercept 4 ; center at origin; passing through $( 4 \sqrt { 5 } , 6 )$

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

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

Write an equation for the hyperbola. -vertices $( - 6 , - 2 ) , ( - 6,16 )$ ; eccentricity $\frac { \sqrt { 106 } } { 9 }$