Question 1

Graph the ellipse.
-$$100 x ^ { 2 } + 36 y ^ { 2 } = 3600$$

Accepted Answer

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

Question 2

Write an equation for the parabola with vertex at the origin.
-Through $( 3 , - 6 )$, opening downward

Accepted Answer

A)  $x ^ { 2 } = - \frac { 3 } { 2 } y$ 
B)  $x = - \frac { 2 } { 3 } y ^ { 2 }$ 
C)  $y = \frac { 2 } { 3 } x ^ { 2 }$ 
D)  $x ^ { 2 } = - \frac { 2 } { 3 }$ 
A)  $x ^ { 2 } = - \frac { 3 } { 2 } y$ 
B)  $x = - \frac { 2 } { 3 } y ^ { 2 }$ 
C)  $y = \frac { 2 } { 3 } x ^ { 2 }$ 
D)  $x ^ { 2 } = - \frac { 2 } { 3 }$ A

Question 3

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

Accepted Answer

A)  C: $( 0,0 ) ; F : ( 0 , - 20 ) , ( 0,20 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
B)  C: $( 0,0 ) ; \mathrm { F } : ( - 12,0 ) , ( 12,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
C)  C: $( 0,0 ) ; F : ( - 20,0 ) , ( 20,0 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$ 
D)  C: $( 0,0 ) ; F : ( 0 , - 12 ) , ( 0,12 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
A)  C: $( 0,0 ) ; F : ( 0 , - 20 ) , ( 0,20 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
B)  C: $( 0,0 ) ; \mathrm { F } : ( - 12,0 ) , ( 12,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
C)  C: $( 0,0 ) ; F : ( - 20,0 ) , ( 20,0 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$ 
D)  C: $( 0,0 ) ; F : ( 0 , - 12 ) , ( 0,12 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ A

Question 4

Solve the problem.
-A nuclear cooling tower cross section is a hyperbola having a diameter of $54 \mathrm { ft }$ at the center. The distance between the two foci is $92 \mathrm { ft }$. What is the equation for the hyperbola?

Accepted Answer

A)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 1387 } = 5$ 
B)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 1389 } = 1$ 
C)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 2116 } = 1$ 
D)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 1387 } = 1$ 
A)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 1387 } = 5$ 
B)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 1389 } = 1$ 
C)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 2116 } = 1$ 
D)  $\frac { x ^ { 2 } } { 729 } - \frac { y ^ { 2 } } { 1387 } = 1$

Question 5

Find the eccentricity of the conic section shown in the graph.
- 
Point A: $( - 9,0 )$
Point B: $( \sqrt { 85 } , 0 )$
Point $C : \left( \frac { 9 \sqrt { 13 } } { 2 } , 3 \right)$

Accepted Answer

A)  $\mathrm { e } = \frac { 9 } { \sqrt { 85 } }$ 
B)  $e = \frac { \sqrt { 85 } } { 9 }$ 
C)  $\mathrm { e } = \frac { \sqrt { 85 } } { 81 }$ 
D)  $\mathrm { e } = \frac { \sqrt { 77 } } { 9 }$ 
A)  $\mathrm { e } = \frac { 9 } { \sqrt { 85 } }$ 
B)  $e = \frac { \sqrt { 85 } } { 9 }$ 
C)  $\mathrm { e } = \frac { \sqrt { 85 } } { 81 }$ 
D)  $\mathrm { e } = \frac { \sqrt { 77 } } { 9 }$

Question 6

Identify the type of graph.
-$$x ^ { 2 } - 9 x + y = 0$$

Accepted Answer

A)  The graph is a parabola opening downward. 
B)  The equation has no graph. 
C)  The graph is an ellipse with center $( 0,9 )$. 
D)  The graph is a parabola opening upward. 
A)  The graph is a parabola opening downward. 
B)  The equation has no graph. 
C)  The graph is an ellipse with center $( 0,9 )$. 
D)  The graph is a parabola opening upward.

Question 7

Solve the problem.
-A radio telescope has a parabolic surface. If it is $9 \mathrm {~m}$ deep and $12 \mathrm {~m}$ wide, how far is the focus from the vertex?

Accepted Answer

A)  $1 \mathrm {~m}$ 
B)  $3 \mathrm {~m}$ 
C)  $4 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$ 
A)  $1 \mathrm {~m}$ 
B)  $3 \mathrm {~m}$ 
C)  $4 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$

Question 8

Find the eccentricity of the hyperbola.
-$$x ^ { 2 } - y ^ { 2 } = 49$$

Accepted Answer

A)  $\sqrt { 2 }$ 
B)  0 
C)  1 
D)  $\sqrt { 7 }$ 
A)  $\sqrt { 2 }$ 
B)  0 
C)  1 
D)  $\sqrt { 7 }$

Question 9

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

Accepted Answer

A)  C: $( 0,0 ) ; \mathrm { F } : ( - 25,0 ) , ( 25,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 4 } { 3 } \mathrm { x } , \mathrm { y } = - \frac { 4 } { 3 } \mathrm { x }$ 
B)  C: $( 0,0 ) ; \mathrm { F } : ( 0 , - 20 ) , ( 0,20 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( - 25,0 ) , ( 25,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
D)  C: $( 0,0 ) ; F : ( 0 , - 20 ) , ( 0,20 ) ; A : y = \frac { 4 } { 3 } x , y = - x$ 
A)  C: $( 0,0 ) ; \mathrm { F } : ( - 25,0 ) , ( 25,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 4 } { 3 } \mathrm { x } , \mathrm { y } = - \frac { 4 } { 3 } \mathrm { x }$ 
B)  C: $( 0,0 ) ; \mathrm { F } : ( 0 , - 20 ) , ( 0,20 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( - 25,0 ) , ( 25,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 3 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 3 } { 4 } \mathrm { x }$ 
D)  C: $( 0,0 ) ; F : ( 0 , - 20 ) , ( 0,20 ) ; A : y = \frac { 4 } { 3 } x , y = - x$

Question 10

Solve the problem.
-For a hyperbolic mirror the two foci are $44 \mathrm {~cm}$ apart. The distance of the vertex from one focus is 10 $\mathrm { cm }$ and from the other focus is $34 \mathrm {~cm}$. Position a coordinate system with the origin at the center of the hyperbola and with the foci on the $y$-axis. Find the equation of the hyperbola.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 340 } = 1$ 
B)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 340 } = 1$ 
C)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 340 } = 5$ 
D)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 340 } = 5$ 
A)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 340 } = 1$ 
B)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 340 } = 1$ 
C)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 340 } = 5$ 
D)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 340 } = 5$

Question 11

Write an equation for the ellipse.
-eccentricity $\frac { 5 } { 13 }$; foci at $( 5,0 ) , ( - 5,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 169 } + \frac { y ^ { 2 } } { 144 } = 1$ 
B)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 169 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 144 } = 1$ 
A)  $\frac { x ^ { 2 } } { 169 } + \frac { y ^ { 2 } } { 144 } = 1$ 
B)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 169 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 144 } = 1$

Question 12

Why is it not possible to choose h and k, neither zero, so the parabola f(x) = a(x - h)2 + k
has its vertex at the origin?

Accepted Answer

The only way a parabola can have its ver

Question 13

Solve the problem.
-A rectangular board is 4 units by 20 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Accepted Answer

A)  8.0 units 
B)  0.2 units 
C)  2.0 units 
D)  9.8 units 
A)  8.0 units 
B)  0.2 units 
C)  2.0 units 
D)  9.8 units

Question 14

Solve the problem.
-A comet follows the hyperbolic path described by $\frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 17 } = 1$, where $x$ and $y$ are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path?

Accepted Answer

A)  $2.3$ million mi 
B)  23 million mi 
C)  $6.3$ million mi 
D)  $2.4$ million mi 
A)  $2.3$ million mi 
B)  23 million mi 
C)  $6.3$ million mi 
D)  $2.4$ million mi

Question 15

Write an equation for the parabola with vertex at the origin.
-Focus $( 1,0 )$

Accepted Answer

A)  $y ^ { 2 } = 1 x$ 
B)  $y ^ { 2 } = 4 x$ 
C)  $x ^ { 2 } = 1 y$ 
D)  $x ^ { 2 } = 4 y$ 
A)  $y ^ { 2 } = 1 x$ 
B)  $y ^ { 2 } = 4 x$ 
C)  $x ^ { 2 } = 1 y$ 
D)  $x ^ { 2 } = 4 y$

Question 16

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 a
circle or an ellipse.

Accepted Answer

In the equation of a circle, t

Question 17

Write an equation for the hyperbola.
-$x$-intercepts $\pm 8$, foci at $( - \sqrt { 68 } , 0 ) , ( \sqrt { 68 } , 0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 68 } - \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 68 } = 1$ 
A)  $\frac { x ^ { 2 } } { 68 } - \frac { y ^ { 2 } } { 64 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 68 } = 1$

Question 18

Solve the problem.
-A tunnel is in the shape of a parabola. The maximum height is $36 \mathrm {~m}$ and it is $19 \mathrm {~m}$ wide at the base. What is the vertical clearance $3 \mathrm {~m}$ from the edge of the tunnel?

Accepted Answer

A)  $19.1 \mathrm {~m}$ 
B)  $1.6 \mathrm {~m}$ 
C)  $16.9 \mathrm {~m}$ 
D)  $34.4 \mathrm {~m}$ 
A)  $19.1 \mathrm {~m}$ 
B)  $1.6 \mathrm {~m}$ 
C)  $16.9 \mathrm {~m}$ 
D)  $34.4 \mathrm {~m}$

Question 19

Match the equation of the parabola with the appropriate description.
-$$y = 3 x ^ { 2 } - 2 x + 2$$

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 20

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$5 x ^ { 2 } - y = 8$

Accepted Answer

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

Graph the ellipse. - $100 x ^ { 2 } + 36 y ^ { 2 } = 3600$ $Graph the ellipse. - 100 x ^ { 2 } + 36 y ^ { 2 } = 3600$

Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 6 )$ , opening downward

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

Solve the problem. -A nuclear cooling tower cross section is a hyperbola having a diameter of $54 \mathrm { ft }$ at the center. The distance between the two foci is $92 \mathrm { ft }$ . What is the equation for the hyperbola?

Identify the type of graph. - $x ^ { 2 } - 9 x + y = 0$

Find the eccentricity of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 49$

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

Write an equation for the ellipse. -eccentricity $\frac { 5 } { 13 }$ ; foci at $( 5,0 ) , ( - 5,0 )$

Why is it not possible to choose h and k, neither zero, so the parabola f(x) = a(x - h)2 + k has its vertex at the origin?

Solve the problem. -A rectangular board is 4 units by 20 units. How far from the long side of the board will the foci be located to determine the largest elliptical tabletop?

Write an equation for the parabola with vertex at the origin. -Focus $( 1,0 )$

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 a circle or an ellipse.

Write an equation for the hyperbola. - $x$ -intercepts $\pm 8$ , foci at $( - \sqrt { 68 } , 0 ) , ( \sqrt { 68 } , 0 )$

Match the equation of the parabola with the appropriate description. - $y = 3 x ^ { 2 } - 2 x + 2$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $5 x ^ { 2 } - y = 8$

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

Exam 10: Analytic Geometry

Graph the ellipse. - 100x2+36y2=3600100 x ^ { 2 } + 36 y ^ { 2 } = 3600100x2+36y2=3600

Write an equation for the parabola with vertex at the origin. -Through (3,−6)( 3 , - 6 )(3,−6) , opening downward

Find the center, foci, and asymptotes of the hyperbola. - y2256−x2144=1\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 144 } = 1256y2​−144x2​=1

Solve the problem. -A nuclear cooling tower cross section is a hyperbola having a diameter of 54ft54 \mathrm { ft }54ft at the center. The distance between the two foci is 92ft92 \mathrm { ft }92ft . What is the equation for the hyperbola?

Find the eccentricity of the conic section shown in the graph. - Point A: (−9,0)( - 9,0 )(−9,0) Point B: (85,0)( \sqrt { 85 } , 0 )(85​,0) Point C:(9132,3)C : \left( \frac { 9 \sqrt { 13 } } { 2 } , 3 \right)C:(2913​​,3)

Identify the type of graph. - x2−9x+y=0x ^ { 2 } - 9 x + y = 0x2−9x+y=0

Solve the problem. -A radio telescope has a parabolic surface. If it is 9 m9 \mathrm {~m}9 m deep and 12 m12 \mathrm {~m}12 m wide, how far is the focus from the vertex?

Find the eccentricity of the hyperbola. - x2−y2=49x ^ { 2 } - y ^ { 2 } = 49x2−y2=49

Find the center, foci, and asymptotes of the hyperbola. - x2225−y2400=1\frac { x ^ { 2 } } { 225 } - \frac { y ^ { 2 } } { 400 } = 1225x2​−400y2​=1

Write an equation for the ellipse. -eccentricity 513\frac { 5 } { 13 }135​ ; foci at (5,0),(−5,0)( 5,0 ) , ( - 5,0 )(5,0),(−5,0)