Question 1

Name the conic.
-

Accepted Answer

A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  circle 
A)  parabola 
B)  ellipse 
C)  hyperbola 
D)  circle

Question 2

Solve the problem.
-A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the
surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 8 feet across at
its opening and is 2 feet deep at its center, at what position should the receiver be placed?

Accepted Answer

The receiver should

Question 3

Write an equation for the parabola.
-

Accepted Answer

A)  $y ^ { 2 } = 12 x$ 
B)  $y ^ { 2 } = - 12 x$ 
C)  $x ^ { 2 } = - 12 y$ 
D)  $x ^ { 2 } = 12 y$ 
A)  $y ^ { 2 } = 12 x$ 
B)  $y ^ { 2 } = - 12 x$ 
C)  $x ^ { 2 } = - 12 y$ 
D)  $x ^ { 2 } = 12 y$

Question 4

Graph the equation.
-$$( x - 2 ) ^ { 2 } = - 5 ( y + 1 )$$

Accepted Answer

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

Question 5

Find the vertex, focus, and directrix of the parabola.
-

Accepted Answer

A)  vertex: $( 0,0 )$
focus: $( 3,0 )$
directrix: $x = - 3$
  
B)  vertex: $( 0,0 )$
focus: $( 0,3 )$
directrix: $y = - 3$
  
C)  vertex: $( 0,0 )$
focus: $( - 3,0 )$
directrix: $x = 3$
  
D)  vertex: $( 0,0 )$
focus: $( 0,3 )$
directrix: $y = - 3$
  
A)  vertex: $( 0,0 )$
focus: $( 3,0 )$
directrix: $x = - 3$
  
B)  vertex: $( 0,0 )$
focus: $( 0,3 )$
directrix: $y = - 3$
  
C)  vertex: $( 0,0 )$
focus: $( - 3,0 )$
directrix: $x = 3$
  
D)  vertex: $( 0,0 )$
focus: $( 0,3 )$
directrix: $y = - 3$

Question 6

Match the equation to the graph.
-$$( x + 3 ) ^ { 2 } = - 8 ( y - 1 )$$

Accepted Answer

A)  vertex: $( 3 , - 1 )$
focus: $( 1 , - 1 )$
directrix: $x = 5$
  
B)  vertex: $( - 3,1 )$
focus: $( - 3 , - 1 )$
directrix: $y = 3$
  
C)  vertex: $( 3 , - 1 )$
focus: $( 3 , - 3 )$
directrix: $y = 1$
  
D)  vertex: $( - 3,1 )$
focus: $( - 5,1 )$
directrix: $x = - 1$
  
A)  vertex: $( 3 , - 1 )$
focus: $( 1 , - 1 )$
directrix: $x = 5$
  
B)  vertex: $( - 3,1 )$
focus: $( - 3 , - 1 )$
directrix: $y = 3$
  
C)  vertex: $( 3 , - 1 )$
focus: $( 3 , - 3 )$
directrix: $y = 1$
  
D)  vertex: $( - 3,1 )$
focus: $( - 5,1 )$
directrix: $x = - 1$

Question 7

Solve the problem.
-A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.

Accepted Answer

A)  0.90 ft 
B)  0.21 ft 
C)  0.52 ft 
D)  0.26 ft 
A)  0.90 ft 
B)  0.21 ft 
C)  0.52 ft 
D)  0.26 ft

Question 8

Match the equation to the graph.
-$16 y^{2}=4 x^{2}+64$

Accepted Answer

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

Question 9

Graph the ellipse and locate the foci.
-$16 x^{2}+4 y^{2}=64$

Accepted Answer

A)  foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$
  
B)  foci at $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$
  
C)  foci at $( \sqrt { 21 } , 0 )$ and $( - \sqrt { 21 } , 0 )$
  
D)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$
  
A)  foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$
  
B)  foci at $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$
  
C)  foci at $( \sqrt { 21 } , 0 )$ and $( - \sqrt { 21 } , 0 )$
  
D)  foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

Question 10

Match the equation to the graph.
-$$( x + 1 ) ^ { 2 } = 6 ( y + 2 )$$

Accepted Answer

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

Question 11

Solve the problem.
-An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second
Tower. The towers stand 60 inches apart. At a point between the towers and 18 inches along the road from the
Base of one tower, the cable is 1.44 inches above the roadway. Find the height of the towers.

Accepted Answer

A)  11 in. 
B)  9 in. 
C)  8.5 in. 
D)  9.5 in. 
A)  11 in. 
B)  9 in. 
C)  8.5 in. 
D)  9.5 in.

Question 12

Graph the equation.
-$$( y + 1 ) ^ { 2 } = 7 ( x - 1 )$$

Accepted Answer

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

Question 13

Find the center, foci, and vertices of the ellipse.
-$$16 ( x - 3 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$$

Accepted Answer

A)  center at $( 4,1 )$
foci at $( 4,1 - \sqrt { 7 } ) , ( 4,1 + \sqrt { 7 } )$
vertices at $( 4,5 ) , ( 4 , - 3 )$ 
B)  center at $( 1,3 )$
foci at $( 1,3 - \sqrt { 7 } ) , ( 1,3 + \sqrt { 7 } )$
vertices at $( 1,5 ) , ( 1 , - 3 )$ 
C)  center at $( - 3,1 )$
foci at $( - 3,1 - \sqrt { 7 } ) , ( - 3,1 + \sqrt { 7 } )$
vertices at $( - 3,5 ) , ( - 3 , - 3 )$ 
D)  center at $( 3,1 )$
foci at $( 3,1 - \sqrt { 7 } ) , ( 3,1 + \sqrt { 7 } )$
vertices at $( 3,5 ) , ( 3 , - 3 )$ 
A)  center at $( 4,1 )$
foci at $( 4,1 - \sqrt { 7 } ) , ( 4,1 + \sqrt { 7 } )$
vertices at $( 4,5 ) , ( 4 , - 3 )$ 
B)  center at $( 1,3 )$
foci at $( 1,3 - \sqrt { 7 } ) , ( 1,3 + \sqrt { 7 } )$
vertices at $( 1,5 ) , ( 1 , - 3 )$ 
C)  center at $( - 3,1 )$
foci at $( - 3,1 - \sqrt { 7 } ) , ( - 3,1 + \sqrt { 7 } )$
vertices at $( - 3,5 ) , ( - 3 , - 3 )$ 
D)  center at $( 3,1 )$
foci at $( 3,1 - \sqrt { 7 } ) , ( 3,1 + \sqrt { 7 } )$
vertices at $( 3,5 ) , ( 3 , - 3 )$

Question 14

Find the asymptotes of the hyperbola.
-$$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$$

Accepted Answer

A)  $y = \frac { 3 } { 2 } x$ and $y = - \frac { 3 } { 2 } x$ 
B)  $y = \frac { 4 } { 9 } x$ and $y = - \frac { 4 } { 9 } x$ 
C)  $y = \frac { 9 } { 4 } x$ and $y = - \frac { 9 } { 4 } x$ 
D)  $y = \frac { 2 } { 3 } x$ and $y = - \frac { 2 } { 3 } x$ 
A)  $y = \frac { 3 } { 2 } x$ and $y = - \frac { 3 } { 2 } x$ 
B)  $y = \frac { 4 } { 9 } x$ and $y = - \frac { 4 } { 9 } x$ 
C)  $y = \frac { 9 } { 4 } x$ and $y = - \frac { 9 } { 4 } x$ 
D)  $y = \frac { 2 } { 3 } x$ and $y = - \frac { 2 } { 3 } x$

Question 15

Solve the problem.
-The orbit of a planet around a sun is an ellipse with the sun at one focus. The aphelion of a planet is its greatest distance from the sun, its perihelion is its shortest distance, and its mean distance is the length of the semimajor
Axis of the elliptical orbit. If a planet has a perihelion of 402.3 million miles and a mean distance of 404 million miles, write an equation for the orbit of the planet around the sun.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 404 ^ { 2 } } + \frac { y ^ { 2 } } { 403.996 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 404 ^ { 2 } } + \frac { y ^ { 2 } } { 1.7 ^ { 2 } } = 1$ 
C)  $\frac { x ^ { 2 } } { 404.004 ^ { 2 } } + \frac { y ^ { 2 } } { 404 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 404 ^ { 2 } } + \frac { y ^ { 2 } } { 402.3 ^ { 2 } } = 1$ 
A)  $\frac { x ^ { 2 } } { 404 ^ { 2 } } + \frac { y ^ { 2 } } { 403.996 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 404 ^ { 2 } } + \frac { y ^ { 2 } } { 1.7 ^ { 2 } } = 1$ 
C)  $\frac { x ^ { 2 } } { 404.004 ^ { 2 } } + \frac { y ^ { 2 } } { 404 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 404 ^ { 2 } } + \frac { y ^ { 2 } } { 402.3 ^ { 2 } } = 1$

Question 16

Name the conic.
-

Accepted Answer

A)  ellipse 
B)  parabola 
C)  hyperbola 
D)  circle 
A)  ellipse 
B)  parabola 
C)  hyperbola 
D)  circle

Question 17

Find an equation of the parabola described and state the two points that define the latus rectum.
-Focus at (0, 1); directrix the line y = -1

Accepted Answer

A)  x2 = 4y; latus rectum: (2, 1) and (-2, 1) 
B)  x2 = 8y; latus rectum: (4, 1) and (-4, 1) 
C)  x2 = 4y; latus rectum: (1, 2) and (-1, 2) 
D)  y2 = 8x; latus rectum: (3, 4) and (-3, 4) 
A)  x2 = 4y; latus rectum: (2, 1) and (-2, 1) 
B)  x2 = 8y; latus rectum: (4, 1) and (-4, 1) 
C)  x2 = 4y; latus rectum: (1, 2) and (-1, 2) 
D)  y2 = 8x; latus rectum: (3, 4) and (-3, 4)

Question 18

Name the conic.
-Vertex at (0, 0); axis of symmetry the x-axis; containing the point (8, 6)

Accepted Answer

A)  $y ^ { 2 } = \frac { 9 } { 2 } x$ 
B)  $y ^ { 2 } = \frac { 9 } { 8 } x$ 
C)  $x ^ { 2 } = \frac { 9 } { 8 } y$ 
D)  $x ^ { 2 } = \frac { 9 } { 2 } y$ 
A)  $y ^ { 2 } = \frac { 9 } { 2 } x$ 
B)  $y ^ { 2 } = \frac { 9 } { 8 } x$ 
C)  $x ^ { 2 } = \frac { 9 } { 8 } y$ 
D)  $x ^ { 2 } = \frac { 9 } { 2 } y$

Question 19

Solve the problem.
-A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 20 inches across at its opening and is 5 feet deep, where will the light be concentrated?

Accepted Answer

A)  5 in. from the vertex 
B)  1.3 in. from the vertex 
C)  0.6 in. from the vertex 
D)  0.4 in. from the vertex 
A)  5 in. from the vertex 
B)  1.3 in. from the vertex 
C)  0.6 in. from the vertex 
D)  0.4 in. from the vertex

Question 20

Find an equation for the ellipse described. Graph the equation.
-Foci at (-1, 7) and (-1, 1); length of major axis is 10

Accepted Answer

A) 
 
$$\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$$ 
B) 
 
$$\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 1 ) ^ { 2 } } { 16 } = 1$$ 
C) 
  
D) 
 
 $$\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1 \quad \frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$ 
A) 
 
$$\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$$ 
B) 
 
$$\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x + 1 ) ^ { 2 } } { 16 } = 1$$ 
C) 
  
D) 
 
 $$\frac { ( y - 4 ) ^ { 2 } } { 25 } + \frac { ( x - 1 ) ^ { 2 } } { 16 } = 1 \quad \frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 16 } = 1$$

Name the conic. -

Write an equation for the parabola. -

Graph the equation. - $( x - 2 ) ^ { 2 } = - 5 ( y + 1 )$ $Graph the equation. - ( x - 2 ) ^ { 2 } = - 5 ( y + 1 )$

Find the vertex, focus, and directrix of the parabola. -

Match the equation to the graph. - $( x + 3 ) ^ { 2 } = - 8 ( y - 1 )$ $Match the equation to the graph. - ( x + 3 ) ^ { 2 } = - 8 ( y - 1 )$

Solve the problem. -A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.

Match the equation to the graph. - $16 y^{2}=4 x^{2}+64$ $Match the equation to the graph. - 16 y^{2}=4 x^{2}+64$

Graph the ellipse and locate the foci. - $16 x^{2}+4 y^{2}=64$ $Graph the ellipse and locate the foci. - 16 x^{2}+4 y^{2}=64$

Match the equation to the graph. - $( x + 1 ) ^ { 2 } = 6 ( y + 2 )$

Graph the equation. - $( y + 1 ) ^ { 2 } = 7 ( x - 1 )$ $Graph the equation. - ( y + 1 ) ^ { 2 } = 7 ( x - 1 )$

Find the center, foci, and vertices of the ellipse. - $16 ( x - 3 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

Find the asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$

Name the conic. -

Find an equation of the parabola described and state the two points that define the latus rectum. -Focus at (0, 1); directrix the line y = -1

Name the conic. -Vertex at (0, 0); axis of symmetry the x-axis; containing the point (8, 6)

Solve the problem. -A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 20 inches across at its opening and is 5 feet deep, where will the light be concentrated?

Find an equation for the ellipse described. Graph the equation. -Foci at (-1, 7) and (-1, 1); length of major axis is 10

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 5: Conics

Name the conic. -

Write an equation for the parabola. -

Graph the equation. - (x−2)2=−5(y+1)( x - 2 ) ^ { 2 } = - 5 ( y + 1 )(x−2)2=−5(y+1)

Find the vertex, focus, and directrix of the parabola. -

Match the equation to the graph. - (x+3)2=−8(y−1)( x + 3 ) ^ { 2 } = - 8 ( y - 1 )(x+3)2=−8(y−1)

Solve the problem. -A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.

Match the equation to the graph. - 16y2=4x2+6416 y^{2}=4 x^{2}+6416y2=4x2+64

Graph the ellipse and locate the foci. - 16x2+4y2=6416 x^{2}+4 y^{2}=6416x2+4y2=64

Match the equation to the graph. - (x+1)2=6(y+2)( x + 1 ) ^ { 2 } = 6 ( y + 2 )(x+1)2=6(y+2)

Graph the equation. - (y+1)2=7(x−1)( y + 1 ) ^ { 2 } = 7 ( x - 1 )(y+1)2=7(x−1)

Find the center, foci, and vertices of the ellipse. - 16(x−3)2+9(y−1)2=14416 ( x - 3 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 14416(x−3)2+9(y−1)2=144

Find the asymptotes of the hyperbola. - x24−y29=1\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 14x2​−9y2​=1

Name the conic. -

Find an equation of the parabola described and state the two points that define the latus rectum. -Focus at (0, 1); directrix the line y = -1

Name the conic. -Vertex at (0, 0); axis of symmetry the x-axis; containing the point (8, 6)

Solve the problem. -A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 20 inches across at its opening and is 5 feet deep, where will the light be concentrated?

Find an equation for the ellipse described. Graph the equation. -Foci at (-1, 7) and (-1, 1); length of major axis is 10

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Graph the equation. - $( x - 2 ) ^ { 2 } = - 5 ( y + 1 )$ $Graph the equation. - ( x - 2 ) ^ { 2 } = - 5 ( y + 1 )$

Match the equation to the graph. - $( x + 3 ) ^ { 2 } = - 8 ( y - 1 )$ $Match the equation to the graph. - ( x + 3 ) ^ { 2 } = - 8 ( y - 1 )$

Match the equation to the graph. - $16 y^{2}=4 x^{2}+64$ $Match the equation to the graph. - 16 y^{2}=4 x^{2}+64$

Graph the ellipse and locate the foci. - $16 x^{2}+4 y^{2}=64$ $Graph the ellipse and locate the foci. - 16 x^{2}+4 y^{2}=64$

Match the equation to the graph. - $( x + 1 ) ^ { 2 } = 6 ( y + 2 )$

Graph the equation. - $( y + 1 ) ^ { 2 } = 7 ( x - 1 )$ $Graph the equation. - ( y + 1 ) ^ { 2 } = 7 ( x - 1 )$

Find the center, foci, and vertices of the ellipse. - $16 ( x - 3 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

Find the asymptotes of the hyperbola. - $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$