Question 1

Determine the two equations necessary to graph the hyperbola with a graphing calculator.
-$$\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  $y = \frac { 3 \sqrt { x ^ { 2 } - 25 } } { 5 }$ and $y = - \frac { 3 \sqrt { x ^ { 2 } - 25 } } { 5 }$ 
B)  $y = \frac { 5 \sqrt { \mathrm { x } ^ { 2 } + 25 } } { 3 }$ and $y = - \frac { 5 \sqrt { \mathrm { x } ^ { 2 } + 25 } } { 3 }$ 
C)  $y = \frac { 5 \sqrt { \mathrm { x } ^ { 2 } - 25 } } { 3 }$ and $\mathrm { y } = - \frac { 5 \sqrt { \mathrm { x } ^ { 2 } - 25 } } { 3 }$ 
D)  $y = \frac { 3 \sqrt { x ^ { 2 } } - 5 } { 5 }$ and $y = - \frac { 3 \sqrt { x ^ { 2 } } - 5 } { 5 }$ 
A)  $y = \frac { 3 \sqrt { x ^ { 2 } - 25 } } { 5 }$ and $y = - \frac { 3 \sqrt { x ^ { 2 } - 25 } } { 5 }$ 
B)  $y = \frac { 5 \sqrt { \mathrm { x } ^ { 2 } + 25 } } { 3 }$ and $y = - \frac { 5 \sqrt { \mathrm { x } ^ { 2 } + 25 } } { 3 }$ 
C)  $y = \frac { 5 \sqrt { \mathrm { x } ^ { 2 } - 25 } } { 3 }$ and $\mathrm { y } = - \frac { 5 \sqrt { \mathrm { x } ^ { 2 } - 25 } } { 3 }$ 
D)  $y = \frac { 3 \sqrt { x ^ { 2 } } - 5 } { 5 }$ and $y = - \frac { 3 \sqrt { x ^ { 2 } } - 5 } { 5 }$

Question 2

Graph the ellipse.
-$$81 x ^ { 2 } + 9 y ^ { 2 } = 729$$

Accepted Answer

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

Question 3

Give the focus, directrix, and axis for the parabola.
-A building has an entry the shape of a parabolic arch $98 \mathrm { ft }$ high and $6 \mathrm { ft }$ wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Accepted Answer

A)  $y ^ { 2 } = - 0.4 x$ 
B)  $y ^ { 2 } = - 0.1 x$ 
C)  $x ^ { 2 } = - 0.4 y$ 
D)  $x ^ { 2 } = - 0.1 y$ 
A)  $y ^ { 2 } = - 0.4 x$ 
B)  $y ^ { 2 } = - 0.1 x$ 
C)  $x ^ { 2 } = - 0.4 y$ 
D)  $x ^ { 2 } = - 0.1 y$

Question 4

Write an equation for the parabola.
-vertex: $( 4 , - 2 )$, directrix: $x = 9$

Accepted Answer

A)  $x ^ { 2 } = - 20 ( y - 4 )$ 
B)  $( x + 2 ) ^ { 2 } = - 20 ( y - 4 )$ 
C)  $( y - 4 ) ^ { 2 } = - 20 ( x + 2 )$ 
D)  $( y + 2 ) ^ { 2 } = - 20 ( x - 4 )$ 
A)  $x ^ { 2 } = - 20 ( y - 4 )$ 
B)  $( x + 2 ) ^ { 2 } = - 20 ( y - 4 )$ 
C)  $( y - 4 ) ^ { 2 } = - 20 ( x + 2 )$ 
D)  $( y + 2 ) ^ { 2 } = - 20 ( x - 4 )$

Question 5

Write an equation for the ellipse.
-$e = \frac { 9 } { 41 } ;$ foci at $( 9,0 ) , ( - 9,0 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 1600 } + \frac { y ^ { 2 } } { 1681 } = 1$ 
B)  $\frac { x ^ { 2 } } { 1681 } + \frac { y ^ { 2 } } { 1600 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 1600 } = 1$ 
D)  $\frac { x ^ { 2 } } { 1600 } + \frac { y ^ { 2 } } { 81 } = 1$ 
A)  $\frac { x ^ { 2 } } { 1600 } + \frac { y ^ { 2 } } { 1681 } = 1$ 
B)  $\frac { x ^ { 2 } } { 1681 } + \frac { y ^ { 2 } } { 1600 } = 1$ 
C)  $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 1600 } = 1$ 
D)  $\frac { x ^ { 2 } } { 1600 } + \frac { y ^ { 2 } } { 81 } = 1$

Question 6

Write an equation for the parabola with vertex at the origin.
-Through $( \sqrt { 2 } , 2 )$, opening upward

Accepted Answer

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

Question 7

Graph the hyperbola.
-$$\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

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

Question 8

Graph the parabola.
-$$x = y ^ { 2 } - 4$$

Accepted Answer

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

Question 9

Find the eccentricity e of the hyperbola.
-$$8 x ^ { 2 } - 9 y ^ { 2 } = 72$$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { \sqrt { 17 } } { 3 }$ 
C)  $\frac { \sqrt { 13 } } { 3 }$ 
D)  $\frac { 3 } { 2 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { \sqrt { 17 } } { 3 }$ 
C)  $\frac { \sqrt { 13 } } { 3 }$ 
D)  $\frac { 3 } { 2 }$

Question 10

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$5 x ^ { 2 } = 25 - 5 y ^ { 2 }$

Accepted Answer

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

Question 11

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$y ^ { 2 } = 144 - x ^ { 2 }$

Accepted Answer

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

Question 12

Find the eccentricity e of the ellipse.
-A rectangular board is 6 feet by 20 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)  7.0 ft 
B)  0.5 ft 
C)  9.5 ft 
D)  3.0 ft 
A)  7.0 ft 
B)  0.5 ft 
C)  9.5 ft 
D)  3.0 ft

Question 13

Give the focus, directrix, and axis for the parabola.
-$$( y + 4 ) ^ { 2 } = 8 ( x - 1 )$$

Accepted Answer

A)  $( 3 , - 4 ) , x = - 1 , y = - 4$ 
B)  $( - 2,1 ) , x = - 6 , y = 1$ 
C)  $( 1,4 ) , x = - 3 , y = 4$ 
D)  $( - 1 , - 4 ) , x = 3 , y = - 4$ 
A)  $( 3 , - 4 ) , x = - 1 , y = - 4$ 
B)  $( - 2,1 ) , x = - 6 , y = 1$ 
C)  $( 1,4 ) , x = - 3 , y = 4$ 
D)  $( - 1 , - 4 ) , x = 3 , y = - 4$

Question 14

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

Accepted Answer

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

Question 15

Graph the ellipse.
-$$\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

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

Question 16

Graph the ellipse.
-$$\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

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

Question 17

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

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 18

Find the center, foci, and asymptotes of the hyperbola.
-$$\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$$

Accepted Answer

A)  C: $( 0,0 ) ; F : ( - 4,0 ) , ( 4,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
B)  C: $( 0,0 ) ; F : ( - 5,0 ) , ( 5,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
C)  C: $( 0,0 ) ; F : ( 0 , - 4 ) , ( 0,4 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$ 
D)  C: $( 0,0 ) ; F : ( 0 , - 5 ) , ( 0,5 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$ 
A)  C: $( 0,0 ) ; F : ( - 4,0 ) , ( 4,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
B)  C: $( 0,0 ) ; F : ( - 5,0 ) , ( 5,0 ) ; A : y = \frac { 4 } { 3 } x , y = - \frac { 4 } { 3 } x$ 
C)  C: $( 0,0 ) ; F : ( 0 , - 4 ) , ( 0,4 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$ 
D)  C: $( 0,0 ) ; F : ( 0 , - 5 ) , ( 0,5 ) ; A : y = \frac { 3 } { 4 } x , y = - \frac { 3 } { 4 } x$

Question 19

Match the equation of a hyperbola with its description.
-$$\frac { ( y - 3 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 81 } = 1$$

Accepted Answer

A)  center (-1, -3); horizontal transverse axis 
B)  center (-3, -1); horizontal transverse axis 
C)  center (3, 1); vertical transverse axis 
D)  center (1, 3); vertical transverse axis 
A)  center (-1, -3); horizontal transverse axis 
B)  center (-3, -1); horizontal transverse axis 
C)  center (3, 1); vertical transverse axis 
D)  center (1, 3); vertical transverse axis

Question 20

Write an equation for the ellipse.
-center at origin; length of major axis $12 ; \mathrm { y }$-intercepts $( 0 , \pm 5 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$ 
A)  $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 5 } = 1$ 
B)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 36 } = 1$ 
C)  $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 6 } = 1$ 
D)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$

Graph the ellipse. - $81 x ^ { 2 } + 9 y ^ { 2 } = 729$ $Graph the ellipse. - 81 x ^ { 2 } + 9 y ^ { 2 } = 729$

Write an equation for the parabola. -vertex: $( 4 , - 2 )$ , directrix: $x = 9$

Write an equation for the ellipse. - $e = \frac { 9 } { 41 } ;$ foci at $( 9,0 ) , ( - 9,0 )$

Write an equation for the parabola with vertex at the origin. -Through $( \sqrt { 2 } , 2 )$ , opening upward

Graph the hyperbola. - $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 64 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 64 } = 1$

Graph the parabola. - $x = y ^ { 2 } - 4$ $Graph the parabola. - x = y ^ { 2 } - 4$

Find the eccentricity e of the hyperbola. - $8 x ^ { 2 } - 9 y ^ { 2 } = 72$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $5 x ^ { 2 } = 25 - 5 y ^ { 2 }$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $y ^ { 2 } = 144 - x ^ { 2 }$

Find the eccentricity e of the ellipse. -A rectangular board is 6 feet by 20 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.

Give the focus, directrix, and axis for the parabola. - $( y + 4 ) ^ { 2 } = 8 ( x - 1 )$

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

Graph the ellipse. - $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$

Graph the ellipse. - $\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$ $Graph the ellipse. - \frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$

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

Find the center, foci, and asymptotes of the hyperbola. - $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$

Match the equation of a hyperbola with its description. - $\frac { ( y - 3 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 81 } = 1$

Write an equation for the ellipse. -center at origin; length of major axis $12 ; \mathrm { y }$ -intercepts $( 0 , \pm 5 )$

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 hyperbola with a graphing calculator. - x225−y29=1\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 125x2​−9y2​=1

Graph the ellipse. - 81x2+9y2=72981 x ^ { 2 } + 9 y ^ { 2 } = 72981x2+9y2=729

Give the focus, directrix, and axis for the parabola. -A building has an entry the shape of a parabolic arch 98ft98 \mathrm { ft }98ft high and 6ft6 \mathrm { ft }6ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Write an equation for the parabola. -vertex: (4,−2)( 4 , - 2 )(4,−2) , directrix: x=9x = 9x=9

Write an equation for the ellipse. - e=941;e = \frac { 9 } { 41 } ;e=419​; foci at (9,0),(−9,0)( 9,0 ) , ( - 9,0 )(9,0),(−9,0)

Write an equation for the parabola with vertex at the origin. -Through (2,2)( \sqrt { 2 } , 2 )(2​,2) , opening upward

Graph the hyperbola. - x29−y264=1\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 64 } = 19x2​−64y2​=1

Graph the parabola. - x=y2−4x = y ^ { 2 } - 4x=y2−4

Find the eccentricity e of the hyperbola. - 8x2−9y2=728 x ^ { 2 } - 9 y ^ { 2 } = 728x2−9y2=72

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 5x2=25−5y25 x ^ { 2 } = 25 - 5 y ^ { 2 }5x2=25−5y2

Identify the equation as a parabola, circle, ellipse, or hyperbola. - y2=144−x2y ^ { 2 } = 144 - x ^ { 2 }y2=144−x2

Find the eccentricity e of the ellipse. -A rectangular board is 6 feet by 20 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.

Give the focus, directrix, and axis for the parabola. - (y+4)2=8(x−1)( y + 4 ) ^ { 2 } = 8 ( x - 1 )(y+4)2=8(x−1)

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

Graph the ellipse. - x264+y225=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 164x2​+25y2​=1

Graph the ellipse. - (x−1)216+(y+1)29=1\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 116(x−1)2​+9(y+1)2​=1

Match the equation of the parabola with the appropriate description. - x=−3y2+2y+2x = - 3 y ^ { 2 } + 2 y + 2x=−3y2+2y+2

Find the center, foci, and asymptotes of the hyperbola. - y29−x216=1\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 19y2​−16x2​=1

Match the equation of a hyperbola with its description. - (y−3)216−(x−1)281=1\frac { ( y - 3 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 81 } = 116(y−3)2​−81(x−1)2​=1

Write an equation for the ellipse. -center at origin; length of major axis 12;y12 ; \mathrm { y }12;y -intercepts (0,±5)( 0 , \pm 5 )(0,±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

Determine the two equations necessary to graph the hyperbola with a graphing calculator. - $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$

Graph the ellipse. - $81 x ^ { 2 } + 9 y ^ { 2 } = 729$ $Graph the ellipse. - 81 x ^ { 2 } + 9 y ^ { 2 } = 729$

Write an equation for the parabola. -vertex: $( 4 , - 2 )$ , directrix: $x = 9$

Write an equation for the ellipse. - $e = \frac { 9 } { 41 } ;$ foci at $( 9,0 ) , ( - 9,0 )$

Write an equation for the parabola with vertex at the origin. -Through $( \sqrt { 2 } , 2 )$ , opening upward

Graph the hyperbola. - $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 64 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 64 } = 1$

Graph the parabola. - $x = y ^ { 2 } - 4$ $Graph the parabola. - x = y ^ { 2 } - 4$

Find the eccentricity e of the hyperbola. - $8 x ^ { 2 } - 9 y ^ { 2 } = 72$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $5 x ^ { 2 } = 25 - 5 y ^ { 2 }$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $y ^ { 2 } = 144 - x ^ { 2 }$

Give the focus, directrix, and axis for the parabola. - $( y + 4 ) ^ { 2 } = 8 ( x - 1 )$

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

Graph the ellipse. - $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1$

Graph the ellipse. - $\frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$ $Graph the ellipse. - \frac { ( x - 1 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 9 } = 1$

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

Find the center, foci, and asymptotes of the hyperbola. - $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 16 } = 1$

Match the equation of a hyperbola with its description. - $\frac { ( y - 3 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 81 } = 1$

Write an equation for the ellipse. -center at origin; length of major axis $12 ; \mathrm { y }$ -intercepts $( 0 , \pm 5 )$