Question 1

Match the equation of the ellipse with the appropriate description.
-$$\frac { x ^ { 2 } } { 4 } = 1 - \frac { y ^ { 2 } } { 16 }$$

Accepted Answer

A)  $x$-intercepts $( 4,0 ) , ( - 4,0 )$; y-intercepts $( 0,2 ) , ( 0 , - 2 )$ 
B)  $x$-intercepts $( 2,0 ) , ( - 2,0 )$; y-intercepts $( 0,4 ) , ( 0 , - 4 )$ 
C)  $x$-intercepts $( 4,0 ) , ( - 4,0 )$; y-intercepts $( 0,16 ) , ( 0 , - 16 )$ 
D)  x-intercepts $( 16,0 ) , ( - 16,0 )$; y-intercepts $( 0,4 ) , ( 0 , - 4 )$ 
A)  $x$-intercepts $( 4,0 ) , ( - 4,0 )$; y-intercepts $( 0,2 ) , ( 0 , - 2 )$ 
B)  $x$-intercepts $( 2,0 ) , ( - 2,0 )$; y-intercepts $( 0,4 ) , ( 0 , - 4 )$ 
C)  $x$-intercepts $( 4,0 ) , ( - 4,0 )$; y-intercepts $( 0,16 ) , ( 0 , - 16 )$ 
D)  x-intercepts $( 16,0 ) , ( - 16,0 )$; y-intercepts $( 0,4 ) , ( 0 , - 4 )$

Question 2

Provide an appropriate response.
-Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = - 0.1 ( x - 3 ) ^ { 2 }$ is a parabola with....... $\mathrm { x }$-intercept(s). Its vertex is the........ point of the graph and has coordinates.........

Accepted Answer

A)  no; maximum (or highest); $( - 0.1,3 )$ 
B)  one; maximum (or highest); $( 3,0 )$ 
C)  two; maximum (or highest); $( 3,0 )$ 
D)  one; minimum (or lowest); $( 3,0 )$ 
A)  no; maximum (or highest); $( - 0.1,3 )$ 
B)  one; maximum (or highest); $( 3,0 )$ 
C)  two; maximum (or highest); $( 3,0 )$ 
D)  one; minimum (or lowest); $( 3,0 )$

Question 3

Find the eccentricity e of the ellipse.
-A rectangular board is 8 units by 12 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Accepted Answer

A)  2.0 units 
B)  4.5 units 
C)  1.5 units 
D)  4.0 units 
A)  2.0 units 
B)  4.5 units 
C)  1.5 units 
D)  4.0 units

Question 4

Identify the type of graph.
-$$- 3 x ^ { 2 } + 24 x + 2 y ^ { 2 } - 24 y - 48 = - 72$$

Accepted Answer

A)  The graph is the point $( 4,6 )$. 
B)  The graph is a hyperbola opening upward and downward. 
C)  The graph is a circle with center $( 4,6 )$. 
D)  The equation has no graph. 
A)  The graph is the point $( 4,6 )$. 
B)  The graph is a hyperbola opening upward and downward. 
C)  The graph is a circle with center $( 4,6 )$. 
D)  The equation has no graph.

Question 5

Provide an appropriate response.
-A hyperbola has eccentricity 1.

Accepted Answer

A)  False 
B)  True 
A)  False 
B)  True

Question 6

Provide an appropriate response.
-Discuss the symmetries exhibited by an ellipse centered at the origin.

Accepted Answer

An ellipse centered at the ori

Question 7

Identify the type of graph.
-$10 x ^ { 2 } + 60 x + 10 y ^ { 2 } - 20 y = - 99$

Accepted Answer

A)  The graph is the point (-3, 1). 
B)  The equation has no graph. 
C)  The graph is a circle with center (-3, 1). 
D)  The graph is a circle with center (3, -1). 
A)  The graph is the point (-3, 1). 
B)  The equation has no graph. 
C)  The graph is a circle with center (-3, 1). 
D)  The graph is a circle with center (3, -1).

Question 8

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$$x = 2 y ^ { 2 } + 8$$

Accepted Answer

A)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 2 } }$ and $y = - \frac { \sqrt { x - 8 } } { \sqrt { 2 } }$ 
B)  $y = \frac { \sqrt { x - 8 } } { 2 }$ and $y = - \frac { \sqrt { x - 8 } } { 2 }$ 
C)  $y = \sqrt { \frac { x } { 2 } - 8 }$ and $y = - \sqrt { \frac { x } { 2 } - 8 }$ 
D)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 2 } }$ and $y = \frac { \sqrt { 8 - x } } { \sqrt { 2 } }$ 
A)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 2 } }$ and $y = - \frac { \sqrt { x - 8 } } { \sqrt { 2 } }$ 
B)  $y = \frac { \sqrt { x - 8 } } { 2 }$ and $y = - \frac { \sqrt { x - 8 } } { 2 }$ 
C)  $y = \sqrt { \frac { x } { 2 } - 8 }$ and $y = - \sqrt { \frac { x } { 2 } - 8 }$ 
D)  $y = \frac { \sqrt { x - 8 } } { \sqrt { 2 } }$ and $y = \frac { \sqrt { 8 - x } } { \sqrt { 2 } }$

Question 9

Give the focus, directrix, and axis for the parabola.
-$$y ^ { 2 } = 8 x$$

Accepted Answer

A)  $( 2,0 ) , x = - 2 , y$-axis 
B)  $( 0,2 ) , y = - 2 , y$-axis 
C)  $( 2,0 ) , x = - 2 , x$-axis 
D)  $( 2,2 ) , x = 2 , x$-axis 
A)  $( 2,0 ) , x = - 2 , y$-axis 
B)  $( 0,2 ) , y = - 2 , y$-axis 
C)  $( 2,0 ) , x = - 2 , x$-axis 
D)  $( 2,2 ) , x = 2 , x$-axis

Question 10

Give the focus, directrix, and axis for the parabola.
-If an object is thrown upward with an initial velocity of $12 \mathrm { ft }$ per second, then its height is given by $\mathrm { h } = - 12 \mathrm { t } ^ { 2 } + 48 \mathrm { t }$. What is its maximum height?

Accepted Answer

A)  $72 \mathrm { ft }$ 
B)  $48 \mathrm { ft }$ 
C)  $24 \mathrm { ft }$ 
D)  $36 \mathrm { ft }$ 
A)  $72 \mathrm { ft }$ 
B)  $48 \mathrm { ft }$ 
C)  $24 \mathrm { ft }$ 
D)  $36 \mathrm { ft }$

Question 11

Provide an appropriate response.
-Explain in your own words how you can tell from the equation whether the graph is an 
ellipse or a hyperbola.

Accepted Answer

In the equation of an ellipse,

Question 12

Write an equation for the hyperbola.
-$x$-intercepts $( \pm 8,0 )$, foci at $( - \sqrt { 89 } , 0 ) , ( \sqrt { 89 } , 0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 89 } - \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 89 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$ 
A)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1$ 
B)  $\frac { x ^ { 2 } } { 89 } - \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 89 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 64 } = 1$

Question 13

Write an equation for the parabola with vertex at the origin.
-Focus $\left( 0 , - \frac { 1 } { 11 } \right)$

Accepted Answer

A)  $x ^ { 2 } = - 44 y$ 
B)  $x ^ { 2 } = - \frac { 4 } { 11 } y$ 
C)  $y ^ { 2 } = \frac { 1 } { 44 } x$ 
D)  $y ^ { 2 } = - \frac { 4 } { 11 } x$ 
A)  $x ^ { 2 } = - 44 y$ 
B)  $x ^ { 2 } = - \frac { 4 } { 11 } y$ 
C)  $y ^ { 2 } = \frac { 1 } { 44 } x$ 
D)  $y ^ { 2 } = - \frac { 4 } { 11 } x$

Question 14

Match the equation of a hyperbola with its description.
-$$\frac { ( x + 2 ) ^ { 2 } } { 25 } - \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$$

Accepted Answer

A)  center (3, 2); vertical transverse axis 
B)  center (-2, -3); horizontal transverse axis 
C)  center (2, 3); horizontal transverse axis 
D)  center (-3, -2); vertical transverse axis 
A)  center (3, 2); vertical transverse axis 
B)  center (-2, -3); horizontal transverse axis 
C)  center (2, 3); horizontal transverse axis 
D)  center (-3, -2); vertical transverse axis

Question 15

Write an equation for the parabola with vertex at the origin.
-Through $( 5 , - 5 \sqrt { 5 } )$, symmetric with respect to the $x$-axis

Accepted Answer

A)  $y ^ { 2 } = 25 x$ 
B)  $x = \sqrt { 5 } y ^ { 2 }$ 
C)  $x ^ { 2 } = - \sqrt { 5 } y$ 
D)  $x = 25 y ^ { 2 }$ 
A)  $y ^ { 2 } = 25 x$ 
B)  $x = \sqrt { 5 } y ^ { 2 }$ 
C)  $x ^ { 2 } = - \sqrt { 5 } y$ 
D)  $x = 25 y ^ { 2 }$

Question 16

Find the eccentricity of the conic section shown in the graph.
-$x =-4 \sqrt { 3 }$

Accepted Answer

A)  $e = \sqrt { 3 }$ 
B)  $e = 1$ 
C)  $\mathrm { e } = \frac { 4 \sqrt { 3 } } { 3 }$ 
D)  $\mathrm { e } = \frac { \sqrt { 3 } } { 4 }$ 
A)  $e = \sqrt { 3 }$ 
B)  $e = 1$ 
C)  $\mathrm { e } = \frac { 4 \sqrt { 3 } } { 3 }$ 
D)  $\mathrm { e } = \frac { \sqrt { 3 } } { 4 }$

Question 17

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  $y = \sqrt { \frac { 245 - x ^ { 2 } } { 7 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 7 } }$ 
B)  $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$ 
C)  $y = \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$ 
D)  $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$ 
A)  $y = \sqrt { \frac { 245 - x ^ { 2 } } { 7 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 7 } }$ 
B)  $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 7 }$ 
C)  $y = \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$ and $y = - \sqrt { \frac { 175 - x ^ { 2 } } { 5 } }$ 
D)  $y = \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$ and $y = - \frac { 5 \sqrt { 49 - x ^ { 2 } } } { 49 }$

Question 18

Find the center, foci, and asymptotes of the hyperbola.
-$$\frac { ( x + 5 ) ^ { 2 } } { 256 } - \frac { ( y + 1 ) ^ { 2 } } { 144 } = 1$$

Accepted Answer

A)  C: $( - 5 , - 1 ) ; F : ( - 17 , - 1 ) , ( 7 , - 1 ) ; A : y = \frac { 9 } { 16 } x + \frac { 19 } { 64 } , y = - \frac { 9 } { 16 } x + \frac { 19 } { 64 }$ 
B)  C: $( - 5 , - 1 ) ; F : ( - 1 , - 25 ) , ( - 1,15 ) ; A : y = \frac { 4 } { 3 } x - \frac { 11 } { 3 } , y = - \frac { 4 } { 3 } x + \frac { 19 } { 3 }$ 
C)  C: $( - 5 , - 1 ) ; F : ( - 1 , - 17 ) , ( - 1,7 ) ; A : y = \frac { 9 } { 16 } x - \frac { 11 } { 64 } , y = - \frac { 9 } { 16 } x + \frac { 19 } { 64 }$ 
D)  C: $( - 5 , - 1 ) ; F : ( - 25 , - 1 ) , ( 15 , - 1 ) ; A : y = \frac { 3 } { 4 } x + \frac { 11 } { 4 } , y = - \frac { 3 } { 4 } x - \frac { 19 } { 4 }$ 
A)  C: $( - 5 , - 1 ) ; F : ( - 17 , - 1 ) , ( 7 , - 1 ) ; A : y = \frac { 9 } { 16 } x + \frac { 19 } { 64 } , y = - \frac { 9 } { 16 } x + \frac { 19 } { 64 }$ 
B)  C: $( - 5 , - 1 ) ; F : ( - 1 , - 25 ) , ( - 1,15 ) ; A : y = \frac { 4 } { 3 } x - \frac { 11 } { 3 } , y = - \frac { 4 } { 3 } x + \frac { 19 } { 3 }$ 
C)  C: $( - 5 , - 1 ) ; F : ( - 1 , - 17 ) , ( - 1,7 ) ; A : y = \frac { 9 } { 16 } x - \frac { 11 } { 64 } , y = - \frac { 9 } { 16 } x + \frac { 19 } { 64 }$ 
D)  C: $( - 5 , - 1 ) ; F : ( - 25 , - 1 ) , ( 15 , - 1 ) ; A : y = \frac { 3 } { 4 } x + \frac { 11 } { 4 } , y = - \frac { 3 } { 4 } x - \frac { 19 } { 4 }$

Question 19

Find the eccentricity e of the ellipse.
-$$x ^ { 2 } + 25 y ^ { 2 } = 25$$

Accepted Answer

A)  $\frac { \sqrt { 26 } } { 5 }$ 
B)  $\sqrt { 26 }$ 
C)  $\frac { 2 \sqrt { 6 } } { 5 }$ 
D)  $2 \sqrt { 6 }$ 
A)  $\frac { \sqrt { 26 } } { 5 }$ 
B)  $\sqrt { 26 }$ 
C)  $\frac { 2 \sqrt { 6 } } { 5 }$ 
D)  $2 \sqrt { 6 }$

Question 20

Write an equation for the hyperbola.
-vertices at $( - 7,4 ) , ( - 7 , - 16 )$; asymptotes $y = \pm \frac { 10 } { 2 } ( x + 7 ) - 6$

Accepted Answer

A)  $\frac { ( y + 6 ) ^ { 2 } } { 100 } - \frac { ( x + 7 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( y - 6 ) ^ { 2 } } { 100 } - \frac { ( x - 7 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 7 ) ^ { 2 } } { 100 } - \frac { ( y + 6 ) ^ { 2 } } { 100 } = 1$ 
D)  $\frac { ( x - 7 ) ^ { 2 } } { 100 } - \frac { ( y - 6 ) ^ { 2 } } { 100 } = 1$ 
A)  $\frac { ( y + 6 ) ^ { 2 } } { 100 } - \frac { ( x + 7 ) ^ { 2 } } { 4 } = 1$ 
B)  $\frac { ( y - 6 ) ^ { 2 } } { 100 } - \frac { ( x - 7 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( x + 7 ) ^ { 2 } } { 100 } - \frac { ( y + 6 ) ^ { 2 } } { 100 } = 1$ 
D)  $\frac { ( x - 7 ) ^ { 2 } } { 100 } - \frac { ( y - 6 ) ^ { 2 } } { 100 } = 1$

Match the equation of the ellipse with the appropriate description. - $\frac { x ^ { 2 } } { 4 } = 1 - \frac { y ^ { 2 } } { 16 }$

Provide an appropriate response. -Fill in the blanks to complete the statement. The graph of $\mathrm { P } ( \mathrm { x } ) = - 0.1 ( x - 3 ) ^ { 2 }$ is a parabola with....... $\mathrm { x }$ -intercept(s). Its vertex is the........ point of the graph and has coordinates.........

Find the eccentricity e of the ellipse. -A rectangular board is 8 units by 12 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Identify the type of graph. - $- 3 x ^ { 2 } + 24 x + 2 y ^ { 2 } - 24 y - 48 = - 72$

Provide an appropriate response. -A hyperbola has eccentricity 1.

Provide an appropriate response. -Discuss the symmetries exhibited by an ellipse centered at the origin.

Identify the type of graph. - $10 x ^ { 2 } + 60 x + 10 y ^ { 2 } - 20 y = - 99$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 2 y ^ { 2 } + 8$

Give the focus, directrix, and axis for the parabola. - $y ^ { 2 } = 8 x$

Give the focus, directrix, and axis for the parabola. -If an object is thrown upward with an initial velocity of $12 \mathrm { ft }$ per second, then its height is given by $\mathrm { h } = - 12 \mathrm { t } ^ { 2 } + 48 \mathrm { t }$ . What is its maximum height?

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the graph is an ellipse or a hyperbola.

Write an equation for the hyperbola. - $x$ -intercepts $( \pm 8,0 )$ , foci at $( - \sqrt { 89 } , 0 ) , ( \sqrt { 89 } , 0 )$

Write an equation for the parabola with vertex at the origin. -Focus $\left( 0 , - \frac { 1 } { 11 } \right)$

Match the equation of a hyperbola with its description. - $\frac { ( x + 2 ) ^ { 2 } } { 25 } - \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1$

Write an equation for the parabola with vertex at the origin. -Through $( 5 , - 5 \sqrt { 5 } )$ , symmetric with respect to the $x$ -axis

Find the eccentricity of the conic section shown in the graph. - $x =-4 \sqrt { 3 }$ $Find the eccentricity of the conic section shown in the graph. - x =-4 \sqrt { 3 }$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( x + 5 ) ^ { 2 } } { 256 } - \frac { ( y + 1 ) ^ { 2 } } { 144 } = 1$

Find the eccentricity e of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

Write an equation for the hyperbola. -vertices at $( - 7,4 ) , ( - 7 , - 16 )$ ; asymptotes $y = \pm \frac { 10 } { 2 } ( x + 7 ) - 6$

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

Match the equation of the ellipse with the appropriate description. - x24=1−y216\frac { x ^ { 2 } } { 4 } = 1 - \frac { y ^ { 2 } } { 16 }4x2​=1−16y2​

Find the eccentricity e of the ellipse. -A rectangular board is 8 units by 12 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Identify the type of graph. - −3x2+24x+2y2−24y−48=−72- 3 x ^ { 2 } + 24 x + 2 y ^ { 2 } - 24 y - 48 = - 72−3x2+24x+2y2−24y−48=−72

Provide an appropriate response. -A hyperbola has eccentricity 1.

Provide an appropriate response. -Discuss the symmetries exhibited by an ellipse centered at the origin.

Identify the type of graph. - 10x2+60x+10y2−20y=−9910 x ^ { 2 } + 60 x + 10 y ^ { 2 } - 20 y = - 9910x2+60x+10y2−20y=−99

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x=2y2+8x = 2 y ^ { 2 } + 8x=2y2+8

Give the focus, directrix, and axis for the parabola. - y2=8xy ^ { 2 } = 8 xy2=8x

Give the focus, directrix, and axis for the parabola. -If an object is thrown upward with an initial velocity of 12ft12 \mathrm { ft }12ft per second, then its height is given by h=−12t2+48t\mathrm { h } = - 12 \mathrm { t } ^ { 2 } + 48 \mathrm { t }h=−12t2+48t . What is its maximum height?