Question 1

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$ 
A)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$

Question 2

Provide an appropriate response.
-There are some fundamental differences between graphing a hyperbola centered at the 
origin and graphing an ellipse centered at the origin. What are these differences?

Accepted Answer

Answers will vary. One possibility: To g

Question 3

Write an equation for the parabola with vertex at the origin.
-Through $( 6 , - 12 )$, opening downward

Accepted Answer

A)  $y = \frac { 1 } { 3 } x ^ { 2 }$ 
B)  $x = - \frac { 1 } { 3 } y ^ { 2 }$ 
C)  $x ^ { 2 } = - \frac { 1 } { 3 }$ 
D)  $x ^ { 2 } = - 3 y$ 
A)  $y = \frac { 1 } { 3 } x ^ { 2 }$ 
B)  $x = - \frac { 1 } { 3 } y ^ { 2 }$ 
C)  $x ^ { 2 } = - \frac { 1 } { 3 }$ 
D)  $x ^ { 2 } = - 3 y$

Question 4

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 (-2, 0) is one-fourth of the distance from the line x = -9.

Accepted Answer

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

Question 5

Give the focus, directrix, and axis for the parabola.
-A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 19 m wide,
Find the best location for the light source.

Accepted Answer

A)  9 m down from the top 
B)  4.6 m down from the top 
C)  2.3 m down from the top 
D)  6.9 m down from the top 
A)  9 m down from the top 
B)  4.6 m down from the top 
C)  2.3 m down from the top 
D)  6.9 m down from the top

Question 6

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$ 
A)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$ 
D)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Question 7

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { ( y - 2 ) ^ { 2 } } { 36 } - \frac { ( x + 4 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x + 4 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { ( x + 4 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ 
A)  $\frac { ( y - 2 ) ^ { 2 } } { 36 } - \frac { ( x + 4 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x + 4 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$ 
C)  $\frac { ( x + 4 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$ 
D)  $\frac { ( x + 4 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$

Question 8

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

Accepted Answer

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

Question 9

Graph the conic section.
-$$x ^ { 2 } - 14 x - 4 y + 73 = 0$$

Accepted Answer

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

Question 10

Provide an appropriate response.
-In the ellipse $\frac { ( y + 8 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$, what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Accepted Answer

A)  Horizontal: $y = 8$; Vertical: $x = - 9$ 
B)  Horizontal: $y = 9$; Vertical: $x = - 8$ 
C)  Horizontal: $y = 8$; Vertical: $x = 9$ 
D)  Horizontal: $y = - 8$; Vertical: $x = 9$ 
A)  Horizontal: $y = 8$; Vertical: $x = - 9$ 
B)  Horizontal: $y = 9$; Vertical: $x = - 8$ 
C)  Horizontal: $y = 8$; Vertical: $x = 9$ 
D)  Horizontal: $y = - 8$; Vertical: $x = 9$

Question 11

Graph the ellipse.
-$$4 ( x - 2 ) ^ { 2 } + 9 ( y + 1 ) ^ { 2 } = 36$$

Accepted Answer

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

Question 12

Write an equation for the hyperbola.
-A comet follows the hyperbolic path described by $\frac { x ^ { 2 } } { 23 } - \frac { y ^ { 2 } } { 16 } = 1$, 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)  39 million mi 
B)  $7.4$ million mi 
C)  $1.4$ million mi 
D)  $4.8$ million mi 
A)  39 million mi 
B)  $7.4$ million mi 
C)  $1.4$ million mi 
D)  $4.8$ million mi

Question 13

Give the focus, directrix, and axis for the parabola.
-A tunnel is in the shape of a parabola. The maximum height is $34 \mathrm {~m}$ and it is $17 \mathrm {~m}$ wide at the base. What is the vertical clearance $6 \mathrm {~m}$ from the edge of the tunnel?

Accepted Answer

A)  $1.3 \mathrm {~m}$ 
B)  $32.7 \mathrm {~m}$ 
C)  $31.1 \mathrm {~m}$ 
D)  $2.9 \mathrm {~m}$ 
A)  $1.3 \mathrm {~m}$ 
B)  $32.7 \mathrm {~m}$ 
C)  $31.1 \mathrm {~m}$ 
D)  $2.9 \mathrm {~m}$

Question 14

Provide an appropriate response.
-If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave down, how many $\mathrm { x }$-intercepts does the graph have?

Accepted Answer

A)  3 
B)  1 
C)  0 
D)  2 
A)  3 
B)  1 
C)  0 
D)  2

Question 15

Write an equation for the parabola.
-vertex $( - 5 , - 12 )$, focus $( - 5 , - 14 )$

Accepted Answer

A)  $( x - 5 ) ^ { 2 } = - 56 ( y - 12 )$ 
B)  $8 ( y - 5 ) = ( x - 12 ) ^ { 2 }$ 
C)  $( x + 5 ) ^ { 2 } = - 8 ( y + 12 )$ 
D)  $8 ( y - 12 ) = ( x - 5 ) ^ { 2 }$ 
A)  $( x - 5 ) ^ { 2 } = - 56 ( y - 12 )$ 
B)  $8 ( y - 5 ) = ( x - 12 ) ^ { 2 }$ 
C)  $( x + 5 ) ^ { 2 } = - 8 ( y + 12 )$ 
D)  $8 ( y - 12 ) = ( x - 5 ) ^ { 2 }$

Question 16

Give the focus, directrix, and axis for the parabola.
-A radio telescope has a parabolic surface. If it is $ 2 \mathrm{~m} $ deep and $ 16 \mathrm{~m} $ wide, how far is the focus from the vertex?

Accepted Answer

A)  $ 32 \mathrm{~m} $ 
B)  $ 4 \mathrm{~m} $ 
C)  $ 8 \mathrm{~m} $ 
D)  $ 2 \mathrm{~m} $ 
A)  $ 32 \mathrm{~m} $ 
B)  $ 4 \mathrm{~m} $ 
C)  $ 8 \mathrm{~m} $ 
D)  $ 2 \mathrm{~m} $

Question 17

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$3 x = 5 y ^ { 2 } - 26$

Accepted Answer

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

Question 18

Write an equation for the parabola.
-vertex $( 3,2 )$, focus $( 3,4 )$

Accepted Answer

A)  $2 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
B)  $8 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
C)  $y - 2 = 8 ( x - 3 ) ^ { 2 }$ 
D)  $( y - 2 ) ^ { 2 } = 8 ( x - 3 )$ 
A)  $2 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
B)  $8 ( y - 2 ) = ( x - 3 ) ^ { 2 }$ 
C)  $y - 2 = 8 ( x - 3 ) ^ { 2 }$ 
D)  $( y - 2 ) ^ { 2 } = 8 ( x - 3 )$

Question 19

Provide an appropriate response.
-Suppose that $$A = C \neq 0$$ in the equation $$A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$$ 0. What kind of graph 
does this equation have?

Accepted Answer

The equati

Question 20

Provide an appropriate response.
-If an ellipse has vertices at $( - 2,0 ) , ( 2,0 ) , ( 0,1 )$, and $( 0 , - 1 )$, what is its domain? What is its range?

Accepted Answer

A)  Domain: $[ - 2,2 ]$; Range: $[ - 1,1 ]$ 
B)  Domain: [0, 2]; Range: $[ 0,1 ]$ 
C)  Domain: $[ - 2,1 ] ;$ Range: $[ - 1,2 ]$ 
D)  Domain: $[ - 1,1 ] ;$ Range: $[ - 2,2 ]$ 
A)  Domain: $[ - 2,2 ]$; Range: $[ - 1,1 ]$ 
B)  Domain: [0, 2]; Range: $[ 0,1 ]$ 
C)  Domain: $[ - 2,1 ] ;$ Range: $[ - 1,2 ]$ 
D)  Domain: $[ - 1,1 ] ;$ Range: $[ - 2,2 ]$

Choose the equation that matches the graph. -

Provide an appropriate response. -There are some fundamental differences between graphing a hyperbola centered at the origin and graphing an ellipse centered at the origin. What are these differences?

Write an equation for the parabola with vertex at the origin. -Through $( 6 , - 12 )$ , opening downward

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 (-2, 0) is one-fourth of the distance from the line x = -9.

Give the focus, directrix, and axis for the parabola. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 19 m wide, Find the best location for the light source.

Choose the equation that matches the graph. -

Choose the equation that matches the graph. -

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

Graph the conic section. - $x ^ { 2 } - 14 x - 4 y + 73 = 0$ $Graph the conic section. - x ^ { 2 } - 14 x - 4 y + 73 = 0$

Provide an appropriate response. -In the ellipse $\frac { ( y + 8 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$ , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Graph the ellipse. - $4 ( x - 2 ) ^ { 2 } + 9 ( y + 1 ) ^ { 2 } = 36$ $Graph the ellipse. - 4 ( x - 2 ) ^ { 2 } + 9 ( y + 1 ) ^ { 2 } = 36$

Provide an appropriate response. -If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave down, how many $\mathrm { x }$ -intercepts does the graph have?

Write an equation for the parabola. -vertex $( - 5 , - 12 )$ , focus $( - 5 , - 14 )$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $3 x = 5 y ^ { 2 } - 26$

Write an equation for the parabola. -vertex $( 3,2 )$ , focus $( 3,4 )$

Provide an appropriate response. -Suppose that $A = C \neq 0$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$ 0. What kind of graph does this equation have?

Provide an appropriate response. -If an ellipse has vertices at $( - 2,0 ) , ( 2,0 ) , ( 0,1 )$ , and $( 0 , - 1 )$ , what is its domain? What is its range?

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

Choose the equation that matches the graph. -

Provide an appropriate response. -There are some fundamental differences between graphing a hyperbola centered at the origin and graphing an ellipse centered at the origin. What are these differences?

Write an equation for the parabola with vertex at the origin. -Through (6,−12)( 6 , - 12 )(6,−12) , opening downward

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 (-2, 0) is one-fourth of the distance from the line x = -9.

Give the focus, directrix, and axis for the parabola. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 10 m down from the top of the dome the ceiling is 19 m wide, Find the best location for the light source.

Choose the equation that matches the graph. -

Choose the equation that matches the graph. -

Find the eccentricity e of the ellipse. - 4x2+y2=364 x ^ { 2 } + y ^ { 2 } = 364x2+y2=36

Graph the conic section. - x2−14x−4y+73=0x ^ { 2 } - 14 x - 4 y + 73 = 0x2−14x−4y+73=0

Provide an appropriate response. -In the ellipse (y+8)236+(x−9)216=1\frac { ( y + 8 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 136(y+8)2​+16(x−9)2​=1 , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Graph the ellipse. - 4(x−2)2+9(y+1)2=364 ( x - 2 ) ^ { 2 } + 9 ( y + 1 ) ^ { 2 } = 364(x−2)2+9(y+1)2=36

Give the focus, directrix, and axis for the parabola. -A tunnel is in the shape of a parabola. The maximum height is 34 m34 \mathrm {~m}34 m and it is 17 m17 \mathrm {~m}17 m wide at the base. What is the vertical clearance 6 m6 \mathrm {~m}6 m from the edge of the tunnel?

Provide an appropriate response. -If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave down, how many x\mathrm { x }x -intercepts does the graph have?

Write an equation for the parabola. -vertex (−5,−12)( - 5 , - 12 )(−5,−12) , focus (−5,−14)( - 5 , - 14 )(−5,−14)

Give the focus, directrix, and axis for the parabola. -A radio telescope has a parabolic surface. If it is 2 m 2 \mathrm{~m} 2 m deep and 16 m 16 \mathrm{~m} 16 m wide, how far is the focus from the vertex?

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 3x=5y2−263 x = 5 y ^ { 2 } - 263x=5y2−26

Write an equation for the parabola. -vertex (3,2)( 3,2 )(3,2) , focus (3,4)( 3,4 )(3,4)

Provide an appropriate response. -Suppose that A=C≠0A = C \neq 0A=C=0 in the equation Ax2+Bx+Cy2+Dy+E=0A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0Ax2+Bx+Cy2+Dy+E=0 0. What kind of graph does this equation have?

Provide an appropriate response. -If an ellipse has vertices at (−2,0),(2,0),(0,1)( - 2,0 ) , ( 2,0 ) , ( 0,1 )(−2,0),(2,0),(0,1) , and (0,−1)( 0 , - 1 )(0,−1) , what is its domain? What is its range?

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

Write an equation for the parabola with vertex at the origin. -Through $( 6 , - 12 )$ , opening downward

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

Graph the conic section. - $x ^ { 2 } - 14 x - 4 y + 73 = 0$ $Graph the conic section. - x ^ { 2 } - 14 x - 4 y + 73 = 0$

Provide an appropriate response. -In the ellipse $\frac { ( y + 8 ) ^ { 2 } } { 36 } + \frac { ( x - 9 ) ^ { 2 } } { 16 } = 1$ , what is the equation of the horizontal axis of symmetry? The vertical axis of symmetry?

Graph the ellipse. - $4 ( x - 2 ) ^ { 2 } + 9 ( y + 1 ) ^ { 2 } = 36$ $Graph the ellipse. - 4 ( x - 2 ) ^ { 2 } + 9 ( y + 1 ) ^ { 2 } = 36$

Provide an appropriate response. -If the vertex of the graph of a quadratic function lies in quadrant III and the graph is concave down, how many $\mathrm { x }$ -intercepts does the graph have?

Write an equation for the parabola. -vertex $( - 5 , - 12 )$ , focus $( - 5 , - 14 )$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $3 x = 5 y ^ { 2 } - 26$

Write an equation for the parabola. -vertex $( 3,2 )$ , focus $( 3,4 )$

Provide an appropriate response. -Suppose that $A = C \neq 0$ in the equation $A x ^ { 2 } + B x + C y ^ { 2 } + D y + E = 0$ 0. What kind of graph does this equation have?

Provide an appropriate response. -If an ellipse has vertices at $( - 2,0 ) , ( 2,0 ) , ( 0,1 )$ , and $( 0 , - 1 )$ , what is its domain? What is its range?