Question 1

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$$x = 5 y ^ { 2 } - 7 y + 5$$

Accepted Answer

A)  $y = \frac { 7 - \sqrt { 20 x - 51 } } { 10 }$ and $y = \frac { 7 + \sqrt { 20 x - 51 } } { 10 }$ 
B)  $y = \frac { \sqrt { x - 5 } } { - 7 }$ and $y = - \frac { \sqrt { x - 5 } } { - 7 }$ 
C)  $y = \sqrt { \frac { x - 5 } { - 7 } }$ and $y = - \sqrt { \frac { x - 5 } { - 7 } }$ 
D)  $y = \frac { 7 - \sqrt { 20 x - 51 } } { 5 }$ and $y = - \frac { 7 + \sqrt { 20 x - 51 } } { 5 }$ 
A)  $y = \frac { 7 - \sqrt { 20 x - 51 } } { 10 }$ and $y = \frac { 7 + \sqrt { 20 x - 51 } } { 10 }$ 
B)  $y = \frac { \sqrt { x - 5 } } { - 7 }$ and $y = - \frac { \sqrt { x - 5 } } { - 7 }$ 
C)  $y = \sqrt { \frac { x - 5 } { - 7 } }$ and $y = - \sqrt { \frac { x - 5 } { - 7 } }$ 
D)  $y = \frac { 7 - \sqrt { 20 x - 51 } } { 5 }$ and $y = - \frac { 7 + \sqrt { 20 x - 51 } } { 5 }$

Question 2

Give the focus, directrix, and axis for the parabola.
-$$( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$$

Accepted Answer

A)  $( - 2 , - 1 ) , y = 11 , x = 5$ 
B)  $( - 2 , - 1 ) , y = 11 , x = - 2$ 
C)  $( - 8 , - 1 ) , y = 11 , x = - 2$ 
D)  $( - 2 , - 1 ) , y = 11 , x = 6$ 
A)  $( - 2 , - 1 ) , y = 11 , x = 5$ 
B)  $( - 2 , - 1 ) , y = 11 , x = - 2$ 
C)  $( - 8 , - 1 ) , y = 11 , x = - 2$ 
D)  $( - 2 , - 1 ) , y = 11 , x = 6$

Question 3

Give the focus, directrix, and axis for the parabola.
-$$- \frac { 1 } { 36 } x ^ { 2 } = y$$

Accepted Answer

A)  $( 0 , - 9 ) , y = 9 , x$-axis 
B)  $( 0 , - 9 ) , y = 9 , y$-axis 
C)  $( 0,9 ) , y = - 9 , y$-axis 
D)  $( - 18,0 ) , x = 9$, x-axis 
A)  $( 0 , - 9 ) , y = 9 , x$-axis 
B)  $( 0 , - 9 ) , y = 9 , y$-axis 
C)  $( 0,9 ) , y = - 9 , y$-axis 
D)  $( - 18,0 ) , x = 9$, x-axis

Question 4

Graph the hyperbola.
-$$16 x ^ { 2 } - 9 y ^ { 2 } = 144$$

Accepted Answer

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

Question 5

Find the eccentricity e of the ellipse.
-A rectangular board is 19 by 20 units. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the
Length of the string.

Accepted Answer

A)  20 units 
B)  38 units 
C)  19 units 
D)  40 units 
A)  20 units 
B)  38 units 
C)  19 units 
D)  40 units

Question 6

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

Accepted Answer

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

Question 7

Graph the hyperbola.
-$36 y^{2}-16 x^{2}=576$

Accepted Answer

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

Question 8

Graph the ellipse.
-$$4 x ^ { 2 } + 64 y ^ { 2 } = 256$$

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find the eccentricity e of the hyperbola.
-$$x ^ { 2 } - 16 y ^ { 2 } = 1$$

Accepted Answer

A)  4 
B)  $\sqrt { 17 }$ 
C)  17 
D)  $\frac { \sqrt { 17 } } { 4 }$ 
A)  4 
B)  $\sqrt { 17 }$ 
C)  17 
D)  $\frac { \sqrt { 17 } } { 4 }$

Question 11

Match the equation of the ellipse with the appropriate description.
-$$36 x ^ { 2 } = 2916 - 9 y ^ { 2 }$$

Accepted Answer

A)  $x$-intercepts $( 2,0 ) , ( - 2,0 )$; y-intercepts $( 0,18 ) , ( 0 , - 18 )$ 
B)  $x$-intercepts $( 81,0 ) , ( - 81,0 )$; y-intercepts $( 0,324 ) , ( 0 , - 324 )$ 
C)  $x$-intercepts $( 9,0 ) , ( - 9,0 ) ; y$-intercepts $( 0,54 ) , ( 0 , - 54 )$ 
D)  x-intercepts $( 9,0 ) , ( - 9,0 ) ; y$-intercepts $( 0,18 ) , ( 0 , - 18 )$ 
A)  $x$-intercepts $( 2,0 ) , ( - 2,0 )$; y-intercepts $( 0,18 ) , ( 0 , - 18 )$ 
B)  $x$-intercepts $( 81,0 ) , ( - 81,0 )$; y-intercepts $( 0,324 ) , ( 0 , - 324 )$ 
C)  $x$-intercepts $( 9,0 ) , ( - 9,0 ) ; y$-intercepts $( 0,54 ) , ( 0 , - 54 )$ 
D)  x-intercepts $( 9,0 ) , ( - 9,0 ) ; y$-intercepts $( 0,18 ) , ( 0 , - 18 )$

Question 12

Give the focus, directrix, and axis for the parabola.
-$$( x + 9 ) ^ { 2 } = 8 y$$

Accepted Answer

A)  $( - 9 , - 2 ) , y = - 2 , x = - 9$ 
B)  $( - 9,0 ) , y = 2 , x = - 9$ 
C)  $( 9,2 ) , y = 2 , x = 9$ 
D)  $( - 9,2 ) , y = - 2 , x = - 9$ 
A)  $( - 9 , - 2 ) , y = - 2 , x = - 9$ 
B)  $( - 9,0 ) , y = 2 , x = - 9$ 
C)  $( 9,2 ) , y = 2 , x = 9$ 
D)  $( - 9,2 ) , y = - 2 , x = - 9$

Question 13

Provide an appropriate response.
-Explain the differences between an ellipse and a hyperbola. Both definitions emphasize 
distance, but how is distance used differently in these two definitions?

Accepted Answer

Answers will vary. One possibility: An e

Question 14

Match the equation of the ellipse with the appropriate description.
-$$\frac { x ^ { 2 } } { 49 } = 1 - \frac { y ^ { 2 } } { 25 }$$

Accepted Answer

A)  x-intercepts $( 25,0 ) , ( - 25,0 ) ; y$-intercepts $( 0,49 ) , ( 0 , - 49 )$ 
B)  x-intercepts $( 5,0 ) , ( - 5,0 )$; y-intercepts $( 0,7 , ( 0 , - 7 )$ 
C)  $x$-intercepts $( 7,0 ) , ( - 7,0 )$; y-intercepts $( 0,5 ) , ( 0 , - 5 )$ 
D)  x-intercepts $( 49,0 ) , ( - 49,0 )$; y-intercepts $( 0,5 ) , ( 0 , - 5 )$ 
A)  x-intercepts $( 25,0 ) , ( - 25,0 ) ; y$-intercepts $( 0,49 ) , ( 0 , - 49 )$ 
B)  x-intercepts $( 5,0 ) , ( - 5,0 )$; y-intercepts $( 0,7 , ( 0 , - 7 )$ 
C)  $x$-intercepts $( 7,0 ) , ( - 7,0 )$; y-intercepts $( 0,5 ) , ( 0 , - 5 )$ 
D)  x-intercepts $( 49,0 ) , ( - 49,0 )$; y-intercepts $( 0,5 ) , ( 0 , - 5 )$

Question 15

Provide an appropriate response.
-$$\text { Discuss the graph of the equation } \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \text { if } a = b \text {. }$$

Accepted Answer

If a = b, the graph

Question 16

Write an equation for the hyperbola.
-vertices at $( 1 , - 2 )$ and $( 9 , - 2 )$, passing through the point $( - 5,16 )$

Accepted Answer

A)  $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { \frac { 544 } { 7 } } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { \frac { 544 } { 7 } } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { \frac { 432 } { 7 } } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { \frac { 432 } { 7 } } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
A)  $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { \frac { 544 } { 7 } } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { \frac { 544 } { 7 } } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 2 ) ^ { 2 } } { \frac { 432 } { 7 } } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { \frac { 432 } { 7 } } - \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$

Question 17

Identify the type of graph.
-$\frac { x ^ { 2 } } { 11 } = 1 + \frac { y ^ { 2 } } { 5 }$

Accepted Answer

A)  The graph is a hyperbola that opens to the right and left. 
B)  The graph is a hyperbola that opens upward and downward. 
C)  The graph is an ellipse with foci on the x-axis. 
D)  The graph is an ellipse with foci on the y-axis. 
A)  The graph is a hyperbola that opens to the right and left. 
B)  The graph is a hyperbola that opens upward and downward. 
C)  The graph is an ellipse with foci on the x-axis. 
D)  The graph is an ellipse with foci on the y-axis.

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 5 y ^ { 2 } - 7 y + 5$

Give the focus, directrix, and axis for the parabola. - $( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$

Give the focus, directrix, and axis for the parabola. - $- \frac { 1 } { 36 } x ^ { 2 } = y$

Graph the hyperbola. - $16 x ^ { 2 } - 9 y ^ { 2 } = 144$ $Graph the hyperbola. - 16 x ^ { 2 } - 9 y ^ { 2 } = 144$

Find the eccentricity e of the ellipse. -A rectangular board is 19 by 20 units. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the Length of the string.

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

Graph the hyperbola. - $36 y^{2}-16 x^{2}=576$ $Graph the hyperbola. - 36 y^{2}-16 x^{2}=576$

Graph the ellipse. - $4 x ^ { 2 } + 64 y ^ { 2 } = 256$ $Graph the ellipse. - 4 x ^ { 2 } + 64 y ^ { 2 } = 256$

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

Find the eccentricity e of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } = 1$

Match the equation of the ellipse with the appropriate description. - $36 x ^ { 2 } = 2916 - 9 y ^ { 2 }$

Give the focus, directrix, and axis for the parabola. - $( x + 9 ) ^ { 2 } = 8 y$

Provide an appropriate response. -Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Match the equation of the ellipse with the appropriate description. - $\frac { x ^ { 2 } } { 49 } = 1 - \frac { y ^ { 2 } } { 25 }$

Provide an appropriate response. - $\text { Discuss the graph of the equation } \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \text { if } a = b \text {. }$

Write an equation for the hyperbola. -vertices at $( 1 , - 2 )$ and $( 9 , - 2 )$ , passing through the point $( - 5,16 )$

Identify the type of graph. - $\frac { x ^ { 2 } } { 11 } = 1 + \frac { y ^ { 2 } } { 5 }$

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

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x=5y2−7y+5x = 5 y ^ { 2 } - 7 y + 5x=5y2−7y+5

Give the focus, directrix, and axis for the parabola. - (x+2)2=−24(y−5)( x + 2 ) ^ { 2 } = - 24 ( y - 5 )(x+2)2=−24(y−5)

Give the focus, directrix, and axis for the parabola. - −136x2=y- \frac { 1 } { 36 } x ^ { 2 } = y−361​x2=y

Graph the hyperbola. - 16x2−9y2=14416 x ^ { 2 } - 9 y ^ { 2 } = 14416x2−9y2=144

Find the eccentricity e of the ellipse. -A rectangular board is 19 by 20 units. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the Length of the string.

Match the equation of the parabola with the appropriate description. - y=2+4x−x2y = 2 + 4 x - x ^ { 2 }y=2+4x−x2

Graph the hyperbola. - 36y2−16x2=57636 y^{2}-16 x^{2}=57636y2−16x2=576

Graph the ellipse. - 4x2+64y2=2564 x ^ { 2 } + 64 y ^ { 2 } = 2564x2+64y2=256

Graph the hyperbola. - (y−2)24−(x+1)236=1\frac { ( y - 2 ) ^ { 2 } } { 4 } - \frac { ( x + 1 ) ^ { 2 } } { 36 } = 14(y−2)2​−36(x+1)2​=1

Find the eccentricity e of the hyperbola. - x2−16y2=1x ^ { 2 } - 16 y ^ { 2 } = 1x2−16y2=1

Match the equation of the ellipse with the appropriate description. - 36x2=2916−9y236 x ^ { 2 } = 2916 - 9 y ^ { 2 }36x2=2916−9y2

Give the focus, directrix, and axis for the parabola. - (x+9)2=8y( x + 9 ) ^ { 2 } = 8 y(x+9)2=8y

Provide an appropriate response. -Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Match the equation of the ellipse with the appropriate description. - x249=1−y225\frac { x ^ { 2 } } { 49 } = 1 - \frac { y ^ { 2 } } { 25 }49x2​=1−25y2​

Provide an appropriate response. - Discuss the graph of the equation x2a2+y2b2=1 if a=b. \text { Discuss the graph of the equation } \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \text { if } a = b \text {. } Discuss the graph of the equation a2x2​+b2y2​=1 if a=b.

Write an equation for the hyperbola. -vertices at (1,−2)( 1 , - 2 )(1,−2) and (9,−2)( 9 , - 2 )(9,−2) , passing through the point (−5,16)( - 5,16 )(−5,16)

Identify the type of graph. - x211=1+y25\frac { x ^ { 2 } } { 11 } = 1 + \frac { y ^ { 2 } } { 5 }11x2​=1+5y2​

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

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 5 y ^ { 2 } - 7 y + 5$

Give the focus, directrix, and axis for the parabola. - $( x + 2 ) ^ { 2 } = - 24 ( y - 5 )$

Give the focus, directrix, and axis for the parabola. - $- \frac { 1 } { 36 } x ^ { 2 } = y$

Graph the hyperbola. - $16 x ^ { 2 } - 9 y ^ { 2 } = 144$ $Graph the hyperbola. - 16 x ^ { 2 } - 9 y ^ { 2 } = 144$

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

Graph the hyperbola. - $36 y^{2}-16 x^{2}=576$ $Graph the hyperbola. - 36 y^{2}-16 x^{2}=576$

Graph the ellipse. - $4 x ^ { 2 } + 64 y ^ { 2 } = 256$ $Graph the ellipse. - 4 x ^ { 2 } + 64 y ^ { 2 } = 256$

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

Find the eccentricity e of the hyperbola. - $x ^ { 2 } - 16 y ^ { 2 } = 1$

Match the equation of the ellipse with the appropriate description. - $36 x ^ { 2 } = 2916 - 9 y ^ { 2 }$

Give the focus, directrix, and axis for the parabola. - $( x + 9 ) ^ { 2 } = 8 y$

Match the equation of the ellipse with the appropriate description. - $\frac { x ^ { 2 } } { 49 } = 1 - \frac { y ^ { 2 } } { 25 }$

Provide an appropriate response. - $\text { Discuss the graph of the equation } \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 \text { if } a = b \text {. }$

Write an equation for the hyperbola. -vertices at $( 1 , - 2 )$ and $( 9 , - 2 )$ , passing through the point $( - 5,16 )$

Identify the type of graph. - $\frac { x ^ { 2 } } { 11 } = 1 + \frac { y ^ { 2 } } { 5 }$