Question 1

Find the eccentricity of the ellipse.
-$$x ^ { 2 } + 4 y ^ { 2 } = 36$$

Accepted Answer

A)  $\frac { \sqrt { 5 } } { 2 }$ 
B)  $\sqrt { 5 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\sqrt { 3 }$ 
A)  $\frac { \sqrt { 5 } } { 2 }$ 
B)  $\sqrt { 5 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\sqrt { 3 }$

Question 2

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

Accepted Answer

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

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Explain in your own words how you can tell from the equation whether the branches of a
hyperbola open up and down or left and right.

Accepted Answer

The branches open left and rig

Question 4

Write the word or phrase that best completes each statement or answers the question.
-$$36 x ^ { 2 } = 14,400 - 16 y ^ { 2 }$$

Accepted Answer

A)  $x$-intercepts $\pm 20$; $y$-intercepts $\pm 30$ 
B)  $x$-intercepts $\pm 20$; y-intercepts $\pm 120$ 
C)  $x$-intercepts $\pm \frac { 3 } { 2 } ; y$-intercepts $\pm 30$ 
D)  $x$-intercepts $\pm 400$; $y$-intercepts $\pm 900$ 
A)  $x$-intercepts $\pm 20$; $y$-intercepts $\pm 30$ 
B)  $x$-intercepts $\pm 20$; y-intercepts $\pm 120$ 
C)  $x$-intercepts $\pm \frac { 3 } { 2 } ; y$-intercepts $\pm 30$ 
D)  $x$-intercepts $\pm 400$; $y$-intercepts $\pm 900$

Question 5

Using only this graph of $f ( x ) = a ( x - h ) ^ { 2 } + k$, what are the signs of $h$ and $k$ ?

Accepted Answer

A)  $h$ is positive and $k$ is negative. 
B)  $h$ is negative and $k$ is positive. 
C)  Both are positive. 
D)  Both are negative. 
A)  $h$ is positive and $k$ is negative. 
B)  $h$ is negative and $k$ is positive. 
C)  Both are positive. 
D)  Both are negative.

Question 6

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

Accepted Answer

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

Question 7

Write an equation for the parabola.
-vertex $( - 4,6 )$, focus $( - 15,6 )$

Accepted Answer

A)  $- 44 ( x - 4 ) = ( y + 6 ) ^ { 2 }$ 
B)  $x + 4 = - 44 ( y - 6 ) ^ { 2 }$ 
C)  $( y - 6 ) ^ { 2 } = - 44 ( x + 4 )$ 
D)  $x + 6 = - 15 ( y - 4 ) ^ { 2 }$ 
A)  $- 44 ( x - 4 ) = ( y + 6 ) ^ { 2 }$ 
B)  $x + 4 = - 44 ( y - 6 ) ^ { 2 }$ 
C)  $( y - 6 ) ^ { 2 } = - 44 ( x + 4 )$ 
D)  $x + 6 = - 15 ( y - 4 ) ^ { 2 }$

Question 8

Find the center, foci, and asymptotes of the hyperbola.
-$\frac { ( x - 3 ) ^ { 2 } } { 400 } - \frac { ( y - 1 ) ^ { 2 } } { 225 } = 1$

Accepted Answer

A)  C: $( 3,1 ) ; F : ( 1 , - 22 ) , ( 1,28 ) ; A : y = \frac { 4 } { 3 } x + \frac { 5 } { 3 } , y = - \frac { 4 } { 3 } x - \frac { 13 } { 3 }$ 
B)  C: $( 3,1 ) ; F : ( - 22,1 ) , ( 28,1 )$; A: $y = \frac { 3 } { 4 } x - \frac { 5 } { 4 } , y = - \frac { 3 } { 4 } x + \frac { 13 } { 4 }$ 
C)  C: $( 3,1 )$; F: $( 1 , - 12 ) , ( 1,18 ) ; A : y = \frac { 9 } { 16 } x + \frac { 1 } { 16 } , y = - \frac { 9 } { 16 } x - \frac { 13 } { 80 }$ 
D)  C: $( 3,1 ) ; F : ( - 12,1 ) , ( 18,1 )$; A: $y = \frac { 9 } { 16 } x - \frac { 13 } { 80 } , y = - \frac { 9 } { 16 } x - \frac { 13 } { 80 }$ 
A)  C: $( 3,1 ) ; F : ( 1 , - 22 ) , ( 1,28 ) ; A : y = \frac { 4 } { 3 } x + \frac { 5 } { 3 } , y = - \frac { 4 } { 3 } x - \frac { 13 } { 3 }$ 
B)  C: $( 3,1 ) ; F : ( - 22,1 ) , ( 28,1 )$; A: $y = \frac { 3 } { 4 } x - \frac { 5 } { 4 } , y = - \frac { 3 } { 4 } x + \frac { 13 } { 4 }$ 
C)  C: $( 3,1 )$; F: $( 1 , - 12 ) , ( 1,18 ) ; A : y = \frac { 9 } { 16 } x + \frac { 1 } { 16 } , y = - \frac { 9 } { 16 } x - \frac { 13 } { 80 }$ 
D)  C: $( 3,1 ) ; F : ( - 12,1 ) , ( 18,1 )$; A: $y = \frac { 9 } { 16 } x - \frac { 13 } { 80 } , y = - \frac { 9 } { 16 } x - \frac { 13 } { 80 }$

Question 9

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$11 y = 3 ( x + 4 ) ^ { 2 }$$

Accepted Answer

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

Question 10

Match the equation of the parabola with the appropriate description.
-$$y - 13 = 2 ( x + 4 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( 4 , - 13 )$ 
B)  Vertex at $( - 4,13 )$ 
C)  Vertex at $( 13 , - 4 )$ 
D)  Vertex at $( - 13,4 )$ 
A)  Vertex at $( 4 , - 13 )$ 
B)  Vertex at $( - 4,13 )$ 
C)  Vertex at $( 13 , - 4 )$ 
D)  Vertex at $( - 13,4 )$

Question 11

Match the equation of the parabola with the appropriate description.
-$$x = - 4 y ^ { 2 } + 5 y + 2$$

Accepted Answer

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

Question 12

Write the word or phrase that best completes each statement or answers the question.
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 13

Graph the conic section.
-$36(x+2)^{2}+25(y-2)^{2}=900$

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Graph the conic section.
-

Accepted Answer

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

Question 16

Graph the ellipse.
-$$\frac { ( x + 2 ) ^ { 2 } } { 25 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$

Accepted Answer

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

Question 17

Write the word or phrase that best completes each statement or answers the question.
-You have to draw an ellipse such that the length of the major axis is fixed at 20 cm. The
length of the minor axis can have the values 10, 14, or 16 cm. You are told that your ellipse
should be as flat as possible. Which value of length of minor axis would you choose and
why? (Do not calculate).

Accepted Answer

The eccentricity e = c/a shoul

Question 18

It can be shown that an ellipse with foci $( c , 0 )$ and $( - c , 0 )$ where the sum of the distances from any point ( $x , y )$ of the ellipse to the two foci is $2 a$ has equation $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { a ^ { 2 } - c ^ { 2 } } = 1$. Use this result to find an equation of an ellipse with foci $( 3,0 )$ and $( - 3,0 )$, where the sum of the distances from any point of the ellipse to the two foci is 10 .
A) $\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 100 } = 1$
B) $\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 22 } = 1$
C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$
D) $x ^ { 2 } + y ^ { 2 } = 100$

Accepted Answer

The answer of It can be shown that an ellipse...

Question 19

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 absolute value of the difference of the distances from the points $( 0,9 )$ and $( 0 , - 9 )$ is 4 .

Accepted Answer

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

Question 20

Write the word or phrase that best completes each statement or answers the question.
-$$\frac { x ^ { 2 } } { 16 } = 1 - \frac { y ^ { 2 } } { 4 }$$

Accepted Answer

A)  $x$-intercepts $\pm 4 ; y$-intercepts $\pm 2$ 
B)  $x$-intercepts $\pm 16$; $y$-intercepts $\pm 2$ 
C)  $x$-intercepts $\pm 4$; $y$-intercepts $\pm 16$ 
D)  $x$-intercepts $\pm 2$; $\mathrm { y }$-intercepts $\pm 4$ 
A)  $x$-intercepts $\pm 4 ; y$-intercepts $\pm 2$ 
B)  $x$-intercepts $\pm 16$; $y$-intercepts $\pm 2$ 
C)  $x$-intercepts $\pm 4$; $y$-intercepts $\pm 16$ 
D)  $x$-intercepts $\pm 2$; $\mathrm { y }$-intercepts $\pm 4$

Find the eccentricity of the ellipse. - $x ^ { 2 } + 4 y ^ { 2 } = 36$

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

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the branches of a hyperbola open up and down or left and right.

Write the word or phrase that best completes each statement or answers the question. - $36 x ^ { 2 } = 14,400 - 16 y ^ { 2 }$

Using only this graph of $f ( x ) = a ( x - h ) ^ { 2 } + k$ , what are the signs of $h$ and $k$ ? $Using only this graph of f ( x ) = a ( x - h ) ^ { 2 } + k , what are the signs of h and k ?$

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

Write an equation for the parabola. -vertex $( - 4,6 )$ , focus $( - 15,6 )$

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( x - 3 ) ^ { 2 } } { 400 } - \frac { ( y - 1 ) ^ { 2 } } { 225 } = 1$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $11 y = 3 ( x + 4 ) ^ { 2 }$

Match the equation of the parabola with the appropriate description. - $y - 13 = 2 ( x + 4 ) ^ { 2 }$

Match the equation of the parabola with the appropriate description. - $x = - 4 y ^ { 2 } + 5 y + 2$

Write the word or phrase that best completes each statement or answers the question. 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.

Graph the conic section. - $36(x+2)^{2}+25(y-2)^{2}=900$ $Graph the conic section. - 36(x+2)^{2}+25(y-2)^{2}=900$

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

Graph the conic section. -

Graph the ellipse. - $\frac { ( x + 2 ) ^ { 2 } } { 25 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ $Graph the ellipse. - \frac { ( x + 2 ) ^ { 2 } } { 25 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$

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 absolute value of the difference of the distances from the points $( 0,9 )$ and $( 0 , - 9 )$ is 4 .

Write the word or phrase that best completes each statement or answers the question. - $\frac { x ^ { 2 } } { 16 } = 1 - \frac { y ^ { 2 } } { 4 }$

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

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Exam 10: Analytic Geometry

Find the eccentricity of the ellipse. - x2+4y2=36x ^ { 2 } + 4 y ^ { 2 } = 36x2+4y2=36

Identify the equation as a parabola, circle, ellipse, or hyperbola. - x2+y2=36x ^ { 2 } + y ^ { 2 } = 36x2+y2=36

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the branches of a hyperbola open up and down or left and right.

Write the word or phrase that best completes each statement or answers the question. - 36x2=14,400−16y236 x ^ { 2 } = 14,400 - 16 y ^ { 2 }36x2=14,400−16y2

Using only this graph of f(x)=a(x−h)2+kf ( x ) = a ( x - h ) ^ { 2 } + kf(x)=a(x−h)2+k , what are the signs of hhh and kkk ?

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 4x2=4y2+164 x ^ { 2 } = 4 y ^ { 2 } + 164x2=4y2+16

Write an equation for the parabola. -vertex (−4,6)( - 4,6 )(−4,6) , focus (−15,6)( - 15,6 )(−15,6)

Find the center, foci, and asymptotes of the hyperbola. - (x−3)2400−(y−1)2225=1\frac { ( x - 3 ) ^ { 2 } } { 400 } - \frac { ( y - 1 ) ^ { 2 } } { 225 } = 1400(x−3)2​−225(y−1)2​=1

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 11y=3(x+4)211 y = 3 ( x + 4 ) ^ { 2 }11y=3(x+4)2

Match the equation of the parabola with the appropriate description. - y−13=2(x+4)2y - 13 = 2 ( x + 4 ) ^ { 2 }y−13=2(x+4)2

Match the equation of the parabola with the appropriate description. - x=−4y2+5y+2x = - 4 y ^ { 2 } + 5 y + 2x=−4y2+5y+2