Question 1

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

Accepted Answer

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

Question 2

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

A)  $y = \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ 
B)  $x = \sqrt { \frac { 576 - x ^ { 2 } } { 8 } }$ and $x = - \sqrt { \frac { 576 - y ^ { 2 } } { 8 } }$ 
C)  $\mathrm { y } = \frac { 8 \sqrt { 81 - \mathrm { x } ^ { 2 } } } { 81 }$ and $\mathrm { y } = - \frac { 8 \sqrt { 81 + \mathrm { x } ^ { 2 } } } { 81 }$ 
D)  $x = \frac { 9 \sqrt { 81 - y ^ { 2 } } } { 64 }$ and $x = - \frac { 9 \sqrt { 81 - y ^ { 2 } } } { 64 }$ 
A)  $y = \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 81 - x ^ { 2 } } } { 9 }$ 
B)  $x = \sqrt { \frac { 576 - x ^ { 2 } } { 8 } }$ and $x = - \sqrt { \frac { 576 - y ^ { 2 } } { 8 } }$ 
C)  $\mathrm { y } = \frac { 8 \sqrt { 81 - \mathrm { x } ^ { 2 } } } { 81 }$ and $\mathrm { y } = - \frac { 8 \sqrt { 81 + \mathrm { x } ^ { 2 } } } { 81 }$ 
D)  $x = \frac { 9 \sqrt { 81 - y ^ { 2 } } } { 64 }$ and $x = - \frac { 9 \sqrt { 81 - y ^ { 2 } } } { 64 }$

Question 3

Write an equation for the hyperbola.
-center at $( 5 , - 10 )$; focus at $( 5 - 4 \sqrt { 10 } , - 10 ) ; e = \frac { 4 \sqrt { 10 } } { 12 }$

Accepted Answer

A)  $\frac { ( x + 5 ) ^ { 2 } } { 144 } - \frac { ( y - 10 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x + 5 ) ^ { 2 } } { 16 } - \frac { ( y - 10 ) ^ { 2 } } { 144 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 144 } - \frac { ( y + 10 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 10 ) ^ { 2 } } { 144 } = 1$ 
A)  $\frac { ( x + 5 ) ^ { 2 } } { 144 } - \frac { ( y - 10 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x + 5 ) ^ { 2 } } { 16 } - \frac { ( y - 10 ) ^ { 2 } } { 144 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 144 } - \frac { ( y + 10 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 10 ) ^ { 2 } } { 144 } = 1$

Question 4

Find the eccentricity e of the ellipse.
-$$x ^ { 2 } + 2 y ^ { 2 } = 6$$

Accepted Answer

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

Question 5

Write an equation for the hyperbola.
-For a hyperbolic mirror the two foci are $40 \mathrm {~cm}$ apart. The distance of the vertex from one focus is 8 $\mathrm { cm }$ and from the other focus is $32 \mathrm {~cm}$. 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)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 1$ 
B)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 256 } = 1$ 
C)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 5$ 
D)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 256 } = 5$ 
A)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 1$ 
B)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 256 } = 1$ 
C)  $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 5$ 
D)  $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 256 } = 5$

Question 6

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 distance from the point (0, 19) is twice the distance from the line y = 5.

Accepted Answer

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

Question 7

Give the focus, directrix, and axis for the parabola.
-A projectile is thrown upward so that its distance above the ground after $\mathrm { t }$ seconds is $\mathrm { h } = - 15 \mathrm { t } ^ { 2 } + 480 \mathrm { t }$. What is its maximum height?

Accepted Answer

A)  $3840 \mathrm { ft }$ 
B)  $5760 \mathrm { ft }$ 
C)  $2880 \mathrm { ft }$ 
D)  $1920 \mathrm { ft }$ 
A)  $3840 \mathrm { ft }$ 
B)  $5760 \mathrm { ft }$ 
C)  $2880 \mathrm { ft }$ 
D)  $1920 \mathrm { ft }$

Question 8

Match the equation of the parabola with the appropriate description.
-$$y - 8 = 2 ( x + 2 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( - 8,2 )$ 
B)  Vertex at $( 8 , - 2 )$ 
C)  Vertex at $( 2 , - 8 )$ 
D)  Vertex at $( - 2,8 )$ 
A)  Vertex at $( - 8,2 )$ 
B)  Vertex at $( 8 , - 2 )$ 
C)  Vertex at $( 2 , - 8 )$ 
D)  Vertex at $( - 2,8 )$

Question 9

Provide an appropriate response.
-$$\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 16 } = 1 \text { are } ( 9,0 ) \text { and } ( - 9,0 )$$ The y-intercepts of the hyperbola with equation

Accepted Answer

A) True 
 B)False

Question 10

Graph the hyperbola.
-$$\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$$

Accepted Answer

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

Question 11

Provide an appropriate response.
-$$\frac { x ^ { 2 } } { 5476 } + \frac { y ^ { 2 } } { 5184 } = 1$$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Accepted Answer

A)  1.056 
B)  0.231 
C)  0.947 
D)  3.946 
A)  1.056 
B)  0.231 
C)  0.947 
D)  3.946

Question 12

Graph the conic section.
-$$x ^ { 2 } - 14 x - 8 y + 81 = 0$$

Accepted Answer

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

Question 13

Match the equation of the ellipse with the appropriate description.
-$$\frac { 25 x ^ { 2 } } { 9 } + 9 y ^ { 2 } = 900$$

Accepted Answer

A)  $x$-intercepts $( 10,0 ) , ( - 10,0 )$; y-intercepts $( 0,18 ) , ( 0 , - 18 )$ 
B)  $x$-intercepts $( 18,0 ) , ( - 18,0 )$; y-intercepts $( 0,10 ) , ( 0 , - 10 )$ 
C)  $x$-intercepts $( 10,0 ) , ( - 10,0 ) ; y$-intercepts $( 0,30 ) , ( 0 , - 30 )$ 
D)  x-intercepts $( 324,0 ) , ( - 324,0 )$; y-intercepts $( 0,29 ) , ( 0 , - 29 )$ 
A)  $x$-intercepts $( 10,0 ) , ( - 10,0 )$; y-intercepts $( 0,18 ) , ( 0 , - 18 )$ 
B)  $x$-intercepts $( 18,0 ) , ( - 18,0 )$; y-intercepts $( 0,10 ) , ( 0 , - 10 )$ 
C)  $x$-intercepts $( 10,0 ) , ( - 10,0 ) ; y$-intercepts $( 0,30 ) , ( 0 , - 30 )$ 
D)  x-intercepts $( 324,0 ) , ( - 324,0 )$; y-intercepts $( 0,29 ) , ( 0 , - 29 )$

Question 14

Graph the hyperbola.
-$$\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$$

Accepted Answer

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

Question 15

Write an equation for the parabola.
-vertex $( - 9,7 )$, focus $( - 20,7 )$

Accepted Answer

A)  $( y - 7 ) ^ { 2 } = - 44 ( x + 9 )$ 
B)  $x + 9 = - 44 ( y - 7 ) ^ { 2 }$ 
C)  $x + 7 = - 20 ( y - 9 ) ^ { 2 }$ 
D)  $- 44 ( x - 9 ) = ( y + 7 ) ^ { 2 }$ 
A)  $( y - 7 ) ^ { 2 } = - 44 ( x + 9 )$ 
B)  $x + 9 = - 44 ( y - 7 ) ^ { 2 }$ 
C)  $x + 7 = - 20 ( y - 9 ) ^ { 2 }$ 
D)  $- 44 ( x - 9 ) = ( y + 7 ) ^ { 2 }$

Question 16

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

Accepted Answer

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

Question 17

Find the center, foci, and asymptotes of the hyperbola.
-$$x ^ { 2 } - \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

A)  C: $( 0,0 ) ; F : ( 5,0 ) , ( - 5,0 ) ; A : y = \frac { 1 } { 5 } x , y = - \frac { 1 } { 5 } x$ 
B)  C: $( 0,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = 5 x , y = - 5 x$ 
C)  C: $( 0,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = \frac { 1 } { 6 } x , y = - \frac { 1 } { 6 } x$ 
D)  C: $( 5,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = \frac { 1 } { 5 } x , y = - \frac { 1 } { 5 } x$ 
A)  C: $( 0,0 ) ; F : ( 5,0 ) , ( - 5,0 ) ; A : y = \frac { 1 } { 5 } x , y = - \frac { 1 } { 5 } x$ 
B)  C: $( 0,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = 5 x , y = - 5 x$ 
C)  C: $( 0,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = \frac { 1 } { 6 } x , y = - \frac { 1 } { 6 } x$ 
D)  C: $( 5,0 ) ; F : ( \sqrt { 26 } , 0 ) , ( - \sqrt { 26 } , 0 ) ; A : y = \frac { 1 } { 5 } x , y = - \frac { 1 } { 5 } x$

Question 18

Match the equation of the parabola with the appropriate description.
-$$y + 10 = 2 ( x - 15 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( 15 , - 10 )$ 
B)  Vertex at $( - 15,5 )$ 
C)  Vertex at $( - 15,10 )$ 
D)  Vertex at $( 30,10 )$ 
A)  Vertex at $( 15 , - 10 )$ 
B)  Vertex at $( - 15,5 )$ 
C)  Vertex at $( - 15,10 )$ 
D)  Vertex at $( 30,10 )$

Question 19

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

Accepted Answer

A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 144 } = 1$ 
B)  $\frac { x ^ { 2 } } { 169 } + \frac { y ^ { 2 } } { 144 } = 1$ 
C)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 169 } = 1$ 
D)  $\frac { x ^ { 2 } } { 12 } + \frac { y ^ { 2 } } { 13 } = 1$ 
A)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 144 } = 1$ 
B)  $\frac { x ^ { 2 } } { 169 } + \frac { y ^ { 2 } } { 144 } = 1$ 
C)  $\frac { x ^ { 2 } } { 144 } + \frac { y ^ { 2 } } { 169 } = 1$ 
D)  $\frac { x ^ { 2 } } { 12 } + \frac { y ^ { 2 } } { 13 } = 1$

Question 20

Graph the conic section.
-$2 x^{2}+4 y^{2}-28 x+32 y+154=0$

Accepted Answer

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

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

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 1$

Write an equation for the hyperbola. -center at $( 5 , - 10 )$ ; focus at $( 5 - 4 \sqrt { 10 } , - 10 ) ; e = \frac { 4 \sqrt { 10 } } { 12 }$

Find the eccentricity e of the ellipse. - $x ^ { 2 } + 2 y ^ { 2 } = 6$

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 distance from the point (0, 19) is twice the distance from the line y = 5.

Give the focus, directrix, and axis for the parabola. -A projectile is thrown upward so that its distance above the ground after $\mathrm { t }$ seconds is $\mathrm { h } = - 15 \mathrm { t } ^ { 2 } + 480 \mathrm { t }$ . What is its maximum height?

Match the equation of the parabola with the appropriate description. - $y - 8 = 2 ( x + 2 ) ^ { 2 }$

Provide an appropriate response. - $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 16 } = 1 \text { are } ( 9,0 ) \text { and } ( - 9,0 )$ The y-intercepts of the hyperbola with equation

Graph the hyperbola. - $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

Provide an appropriate response. - $\frac { x ^ { 2 } } { 5476 } + \frac { y ^ { 2 } } { 5184 } = 1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Graph the conic section. - $x ^ { 2 } - 14 x - 8 y + 81 = 0$ $Graph the conic section. - x ^ { 2 } - 14 x - 8 y + 81 = 0$

Match the equation of the ellipse with the appropriate description. - $\frac { 25 x ^ { 2 } } { 9 } + 9 y ^ { 2 } = 900$

Graph the hyperbola. - $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$

Write an equation for the parabola. -vertex $( - 9,7 )$ , focus $( - 20,7 )$

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

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - \frac { y ^ { 2 } } { 25 } = 1$

Match the equation of the parabola with the appropriate description. - $y + 10 = 2 ( x - 15 ) ^ { 2 }$

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

Graph the conic section. - $2 x^{2}+4 y^{2}-28 x+32 y+154=0$ $Graph the conic section. - 2 x^{2}+4 y^{2}-28 x+32 y+154=0$

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

Find the eccentricity e of the hyperbola. - x2−25y2=25x ^ { 2 } - 25 y ^ { 2 } = 25x2−25y2=25

Determine the two equations necessary to graph the ellipse with a graphing calculator. - x281+y264=1\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 181x2​+64y2​=1

Write an equation for the hyperbola. -center at (5,−10)( 5 , - 10 )(5,−10) ; focus at (5−410,−10);e=41012( 5 - 4 \sqrt { 10 } , - 10 ) ; e = \frac { 4 \sqrt { 10 } } { 12 }(5−410​,−10);e=12410​​

Find the eccentricity e of the ellipse. - x2+2y2=6x ^ { 2 } + 2 y ^ { 2 } = 6x2+2y2=6

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 distance from the point (0, 19) is twice the distance from the line y = 5.

Give the focus, directrix, and axis for the parabola. -A projectile is thrown upward so that its distance above the ground after t\mathrm { t }t seconds is h=−15t2+480t\mathrm { h } = - 15 \mathrm { t } ^ { 2 } + 480 \mathrm { t }h=−15t2+480t . What is its maximum height?

Match the equation of the parabola with the appropriate description. - y−8=2(x+2)2y - 8 = 2 ( x + 2 ) ^ { 2 }y−8=2(x+2)2

Provide an appropriate response. - x281−y216=1 are (9,0) and (−9,0)\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 16 } = 1 \text { are } ( 9,0 ) \text { and } ( - 9,0 )81x2​−16y2​=1 are (9,0) and (−9,0) The y-intercepts of the hyperbola with equation

Graph the hyperbola. - y29−x236=1\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 19y2​−36x2​=1

Provide an appropriate response. - x25476+y25184=1\frac { x ^ { 2 } } { 5476 } + \frac { y ^ { 2 } } { 5184 } = 15476x2​+5184y2​=1 where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Graph the conic section. - x2−14x−8y+81=0x ^ { 2 } - 14 x - 8 y + 81 = 0x2−14x−8y+81=0

Match the equation of the ellipse with the appropriate description. - 25x29+9y2=900\frac { 25 x ^ { 2 } } { 9 } + 9 y ^ { 2 } = 900925x2​+9y2=900

Graph the hyperbola. - x216−y24=1\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 116x2​−4y2​=1

Write an equation for the parabola. -vertex (−9,7)( - 9,7 )(−9,7) , focus (−20,7)( - 20,7 )(−20,7)

Find the center, foci, and asymptotes of the hyperbola. - x2256−y2144=1\frac { x ^ { 2 } } { 256 } - \frac { y ^ { 2 } } { 144 } = 1256x2​−144y2​=1

Find the center, foci, and asymptotes of the hyperbola. - x2−y225=1x ^ { 2 } - \frac { y ^ { 2 } } { 25 } = 1x2−25y2​=1

Match the equation of the parabola with the appropriate description. - y+10=2(x−15)2y + 10 = 2 ( x - 15 ) ^ { 2 }y+10=2(x−15)2

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

Graph the conic section. - 2x2+4y2−28x+32y+154=02 x^{2}+4 y^{2}-28 x+32 y+154=02x2+4y2−28x+32y+154=0

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

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

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 64 } = 1$

Write an equation for the hyperbola. -center at $( 5 , - 10 )$ ; focus at $( 5 - 4 \sqrt { 10 } , - 10 ) ; e = \frac { 4 \sqrt { 10 } } { 12 }$

Find the eccentricity e of the ellipse. - $x ^ { 2 } + 2 y ^ { 2 } = 6$

Give the focus, directrix, and axis for the parabola. -A projectile is thrown upward so that its distance above the ground after $\mathrm { t }$ seconds is $\mathrm { h } = - 15 \mathrm { t } ^ { 2 } + 480 \mathrm { t }$ . What is its maximum height?

Match the equation of the parabola with the appropriate description. - $y - 8 = 2 ( x + 2 ) ^ { 2 }$

Provide an appropriate response. - $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 16 } = 1 \text { are } ( 9,0 ) \text { and } ( - 9,0 )$ The y-intercepts of the hyperbola with equation

Graph the hyperbola. - $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$ $Graph the hyperbola. - \frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 36 } = 1$

Provide an appropriate response. - $\frac { x ^ { 2 } } { 5476 } + \frac { y ^ { 2 } } { 5184 } = 1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

Graph the conic section. - $x ^ { 2 } - 14 x - 8 y + 81 = 0$ $Graph the conic section. - x ^ { 2 } - 14 x - 8 y + 81 = 0$

Match the equation of the ellipse with the appropriate description. - $\frac { 25 x ^ { 2 } } { 9 } + 9 y ^ { 2 } = 900$

Graph the hyperbola. - $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$

Write an equation for the parabola. -vertex $( - 9,7 )$ , focus $( - 20,7 )$

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

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - \frac { y ^ { 2 } } { 25 } = 1$

Match the equation of the parabola with the appropriate description. - $y + 10 = 2 ( x - 15 ) ^ { 2 }$

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

Graph the conic section. - $2 x^{2}+4 y^{2}-28 x+32 y+154=0$ $Graph the conic section. - 2 x^{2}+4 y^{2}-28 x+32 y+154=0$