Deck 5: Conics

Question 1

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

A)

B)

C)

D)

Answer 1

D

Question 2

Name the conic.
$$x ^ { 2 } = 9 y$$

A)

B)

C)

D)

Answer 2

B

Question 3

Name the conic.
$$x ^ { 2 } = - 14 y$$

A)

B)

C)

D)

Answer 3

B

Question 4

Write an equation for the parabola.

A) y² = 4x
B) y² = -4x
C) x² = -4y
D) x² = 4y

Question 5

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

Match the equation to the graph.
A) vertex: $( - 4 , - 4 )$
focus: $( - 4 , - 7 )$
directrix: $\mathrm { y } = - 1$

B) vertex: $( - 4 , - 4 )$
focus: $( - 4 , - 1 )$
directrix: $y = - 7$

C) vertex: $( - 4 , - 4 )$
focus: $( - 7 , - 4 )$
directrix: $x = - 1$

D) vertex: $( - 4 , - 4 )$
focus: $( - 1 , - 4 )$
directrix: $x = - 7$

Question 7

Match the equation to the graph.
A) vertex: $( 5,3 )$
focus: $( 8,3 )$
directrix: $x = 2$

B) vertex: $( 5,3 )$
focus: $( 5,6 )$
directrix: $\mathrm { y } = 0$


C) vertex: $( 5,3 )$
focus: $( 2,3 )$
directrix: $x = 8$

D) vertex: $( 5,3 )$
focus: $( 5,0 )$
directrix: $y = 6$

Question 8

Write an equation for the parabola.
A) $y ^ { 2 } = 12 x$
В) $y ^ { 2 } = - 12 x$
C) $x ^ { 2 } = - 12 y$
D) $x ^ { 2 } = 12 y$

Question 9

Graph the equation.
$y^{2}=6 x$

A)

B)

C)

D)

Question 10

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

A)

B)

C)

D)

Question 11

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

A)

B)

C)

D)

Question 12

Find the vertex, focus, and directrix of the parabola.
$$x ^ { 2 } = - 12 y$$

C) vertex: $( 0,0 )$
focus: $( 0,3 )$
directrix: $y = - 3$

D) vertex: $( 0,0 )$
focus: $( - 3,0 )$
directrix: $x = 3$

Question 13

Find the vertex, focus, and directrix of the parabola.
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 14

Name the conic.

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

Question 15

Name the conic.

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

Question 16

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

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 17

Graph the equation.
$y^{2}=-12 x$

A)

B)

C)

D)

Question 18

Name the conic.

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

Question 19

Name the conic.

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

Question 20

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

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 21

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

A)

B)

C)

D)

Question 22

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

A)

B)

C)

D)

Question 23

Graph the equation.
$$( x - 2 ) ^ { 2 } = 8 ( y + 1 )$$

A)

B)

C)

D)

Question 24

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

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 25

Graph the ellipse and locate the foci.
$$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$$

A) foci at $( 0 , \sqrt { 5 } )$ and $( 0 , - \sqrt { 5 } )$

B) foci at $( \sqrt { 13 } , 0 )$ and $( - \sqrt { 13 } , 0 )$

C) foci at $( \sqrt { 5 } , 0 )$ and $( - \sqrt { 5 } , 0 )$

D) foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

Question 26

Find the center, foci, and vertices of the ellipse.
$$\frac { ( x - 3 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$$

A) center at $( 3 , - 3 )$
foci at $( 3 + 3 \sqrt { 3 } , - 3 ) , ( 3 - 3 \sqrt { 3 } , - 3 )$
vertices at $( - 3 , - 3 ) , ( 9 , - 3 )$
B) center at $( 3 , - 3 )$
foci at $( - 3 \sqrt { 3 } , - 3 ) , ( 3 \sqrt { 3 } , - 3 )$
vertices at $( 6 , - 3 ) , ( - 6 , - 3 )$
C) center at $( - 3,3 )$
foci at $( - 3 + 3 \sqrt { 3 } , 3 ) , ( - 3 - 3 \sqrt { 3 } , 3 )$
vertices at $( - 3 , - 3 ) , ( 9 , - 3 )$
D) center at $( 3 , - 3 )$
foci at $( 3 + 3 \sqrt { 3 } , 3 ) , ( 3 - 3 \sqrt { 3 } , 3 )$
vertices at $( 6 , - 3 ) , ( - 6 , - 3 )$

Question 27

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?

Question 28

Solve the problem.
A searchlight is shaped like a paraboloid of revolution. If the light source is located 5 feet from the base along the axis of symmetry and the opening is 14 feet across, how deep should the searchlight be?

A) 12.3 ft
B) 2.5 ft
C) 9.8 ft
D) 0.9 ft

Question 29

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

A)

B)

C)

D)

Question 30

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.

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

Question 31

Solve the problem.
A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 142 feet and a maximum height of 25 feet. Find the height of the arch at 25 feet from its center.

A) 21.9 ft
B) 0.8 ft
C) 71 ft
D) 12.4 ft

Question 32

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.

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

Question 33

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?

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 34

Write an equation for the graph.
A) $\frac { ( x - 2 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 16 } = 1$
B) $\frac { ( x + 1 ) ^ { 2 } } { 16 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( x - 2 ) ^ { 2 } } { 16 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$
D) $\frac { ( x + 2 ) ^ { 2 } } { 16 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$

Question 35

Solve the problem.
A sealed-beam headlight is in the shape of a paraboloid of revolution. The bulb, which is placed at the focus, is
3 centimeters from the vertex. If the depth is to be 6 centimeters, what is the diameter of the headlight at its
opening?

Question 36

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

A) foci at $( \sqrt { 21 } , 0 )$ and $( - \sqrt { 21 } , 0 )$

B) foci at $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$

C) foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

D) foci at $( 0,2 \sqrt { 3 } )$ and $( 0 , - 2 \sqrt { 3 } )$

Question 37

Solve the problem.
A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 30 feet and the distance across the top of the mirror is 50 inches, how deep is the mirror in the center? A) 9 in.
B) $\frac { 125 } { 288 } \mathrm { in }$ .
C) $\frac { 125 } { 3456 }$ in.
D) $\frac { 125 } { 24 } \mathrm { in } .$

Question 38

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 are both 12.25 inches tall and stand 70 inches apart. Find the vertical distance from the
Roadway to the cable at a point on the road 14 inches from the lowest point of the cable.

A) 1.76 in.
B) 7.84 in.
C) 2.16 in.
D) 1.96 in.

Question 39

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 are both 9 inches tall and stand 60 inches apart. At some point along the road from the lowest
Point of the cable, the cable is 0.81 inches above the roadway. Find the distance between that point and the base
Of the nearest tower.

A) 21.2 in.
B) 9.2 in.
C) 21 in.
D) 8.8 in.

Question 40

Graph the ellipse and locate the foci.
$$\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$$

A) foci at $( 2 \sqrt { 3 } , 0 )$ and $( - 2 \sqrt { 3 } , 0 )$

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 $( 2 \sqrt { 5 } , 0 )$ and $( - 2 \sqrt { 5 } , 0 )$

Question 41

Find an equation for the ellipse described. Graph the equation.
Foci at (1, 3) and (-5, 3); vertex at (-9, 3)

A) $\frac { ( x + 2 ) ^ { 2 } } { 49 } + \frac { ( y - 3 ) ^ { 2 } } { 40 } = 1$

B) $\frac { ( x - 3 ) ^ { 2 } } { 49 } + \frac { ( y + 2 ) ^ { 2 } } { 40 } = 1$

C) $\frac { ( x + 2 ) ^ { 2 } } { 40 } + \frac { ( y - 3 ) ^ { 2 } } { 49 } = 1$

D) $\frac { ( x - 3 ) ^ { 2 } } { 40 } + \frac { ( y + 2 ) ^ { 2 } } { 49 } = 1$

Question 42

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

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)

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

Question 43

Find the center, foci, and vertices of the ellipse.
$$25 x ^ { 2 } + y ^ { 2 } - 450 x + 2000 = 0$$

A) $( x - 9 ) ^ { 2 } + \frac { y ^ { 2 } } { 25 } = 1$
center: $( 9,0 )$ ; foci: $( 9,2 \sqrt { 6 } ) , ( 9 , - 2 \sqrt { 6 } )$ ; vertices: $( 9,5 ) , ( 9 , - 5 )$
B) $\frac { x ^ { 2 } } { 25 } + ( y - 9 ) ^ { 2 } = 1$
center: $( 9,0 )$ ; foci: $( 9,2 \sqrt { 6 } ) , ( 9 , - 2 \sqrt { 6 } )$ ; vertices: $( 9,5 ) , ( 9 , - 5 )$
C) $\frac { x ^ { 2 } } { 81 } + ( y - 5 ) ^ { 2 } = 1$
center: $( 5,0 )$ ; foci: $( 5,4 \sqrt { 5 } ) , ( 5 , - 2 \sqrt { 6 } )$ ; vertices: $( 5,9 )$ , $( 5 , - 9 )$
D) $( x - 5 ) ^ { 2 } + \frac { y ^ { 2 } } { 81 } = 1$
center: $( 5,0 )$ ; foci: $( 5,4 \sqrt { 5 } ) , ( 5 , - 4 \sqrt { 5 } )$ ; vertices: $( 5,9 ) , ( 5 , - 9 )$

Question 44

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

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 45

Solve the problem.
An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 30 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 29 feet from the
Center is to be 15 feet above ground?

A) 117.17 ft
B) 116 ft
C) 33.49 ft
D) 66.97 ft

Question 46

Find an equation for the ellipse described. Graph the equation.
Vertices at (5, -4) and (5, 8); length of minor axis is 6

A)

$\frac { ( x + 5 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 9 } = 1$
B)

$$\frac { ( x - 5 ) ^ { 2 } } { 9 } + \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$
C)

$$\frac { ( x - 5 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 36 } = 1$$
D)

$$\frac { ( x - 5 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 9 } = 1$$

Question 47

Find an equation for the ellipse described. Graph the equation.
Center at (-2, 4); focus at (-8, 4); contains the point (-10, 4)

A) $\frac { ( x + 4 ) ^ { 2 } } { 28 } + \frac { ( y - 2 ) ^ { 2 } } { 64 } = 1$

B) $\frac { ( x + 4 ) ^ { 2 } } { 64 } + \frac { ( y - 2 ) ^ { 2 } } { 28 } = 1$

C) $\frac { ( x + 2 ) ^ { 2 } } { 64 } + \frac { ( y - 4 ) ^ { 2 } } { 28 } = 1$

D) $\frac { ( x + 2 ) ^ { 2 } } { 28 } + \frac { ( y - 4 ) ^ { 2 } } { 64 } = 1$

Question 48

Find an equation for the ellipse described. Graph the equation.
Foci at (0, 3) and (6, 3); length of major axis is 10

A)

$\frac { ( y + 3 ) ^ { 2 } } { 25 } + \frac { ( x - 3 ) ^ { 2 } } { 16 } = 1$
B)

$$\frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { ( x + 3 ) ^ { 2 } } { 16 } = 1$$
C)

D)

$$\frac { ( x + 3 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 16 } = 1 \quad \frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$$

Question 49

Find an equation for the ellipse described.
Center at $( 4,5 )$ ; focus at $( 9,5 )$ ; vertex at $( 11,5 )$

A) $\frac { ( x - 4 ) ^ { 2 } } { 100 } + \frac { ( y + 5 ) ^ { 2 } } { 9 } = 2$
B) $\frac { ( x + 4 ) ^ { 2 } } { 49 } + \frac { ( y + 5 ) ^ { 2 } } { 24 } = 1$
C) $\frac { ( x + 4 ) ^ { 2 } } { 25 } - \frac { ( y - 5 ) ^ { 2 } } { 19 } = 1$
D) $\frac { ( x - 4 ) ^ { 2 } } { 49 } + \frac { ( y - 5 ) ^ { 2 } } { 24 } = 1$

Question 50

Match the equation to the graph.
$$\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$$

A)

B)

C)

D)

Question 51

Match the equation to the graph.
$$\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 4 } = 1$$

A)

B)
br>C)

D)

Question 52

Find the center, foci, and vertices of the ellipse.
$$16 ( x - 1 ) ^ { 2 } + 4 ( y + 2 ) ^ { 2 } = 64$$

A)

B)

C)

D)

Question 53

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. 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 54

Solve the problem.
A race track is in the shape of an ellipse 80 feet long and 60 feet wide. What is the width 32 feet from the center?

Question 55

Solve the problem.
An arch in the form of a semiellipse is 52 ft wide at the base and has a height of 20 ft. How wide is the arch at a height of 12 ft above the base?

A) 41.6 ft
B) 17.7 ft
C) 35.5 ft
D) 20.8 ft

Question 56

Find the center, foci, and vertices of the ellipse.
$2 x ^ { 2 } + 5 y ^ { 2 } - 20 x + 30 y + 85 = 0$

A) $\frac { ( x - 5 ) ^ { 2 } } { 2 } + \frac { ( y + 3 ) ^ { 2 } } { 5 } = 1$
center: $( 5 , - 3 )$ ; foci: $( 6.7 , - 3 ) , ( 3.3 , - 3 )$ ; vertices: $( 7.2 , - 3 ) , ( 2.8 , - 3 )$
B) $\frac { ( x - 5 ) ^ { 2 } } { 5 } + \frac { ( y + 3 ) ^ { 2 } } { 2 } = 1$
center: $( - 5,3 )$ ; foci: $( - 3.3,3 ) , ( - 6.7,3 )$ ; vertices: $( - 7.2,3 ) , ( - 2.8,3 )$
C) $\frac { ( x - 5 ) ^ { 2 } } { 2 } + \frac { ( y + 3 ) ^ { 2 } } { 5 } = 1$
center: $( - 5,3 )$ ; foci: $( - 3.3,3 ) , ( - 6.7,3 )$ ; vertices: $( - 7.2,3 ) , ( - 2.8,3 )$
D) $\frac { ( x - 5 ) ^ { 2 } } { 5 } + \frac { ( y + 3 ) ^ { 2 } } { 2 } = 1$
center: $( 5 , - 3 )$ ; foci: $( 6.7 , - 3 ) , ( 3.3 , - 3 )$ ; vertices: $( 7.2 , - 3 ) , ( 2.8 , - 3 )$

Question 57

Find an equation for the ellipse described.
Vertices at (-2, 4) and (12, 4); focus at (10, 4) A) $\frac { ( x - 4 ) ^ { 2 } } { 36 } + \frac { ( y - 5 ) ^ { 2 } } { 23 } = 1$
B) $\frac { ( x - 5 ) ^ { 2 } } { 81 } - \frac { ( y + 4 ) ^ { 2 } } { 29 } = 1$
C) $\frac { ( x - 5 ) ^ { 2 } } { 49 } + \frac { ( y - 4 ) ^ { 2 } } { 24 } = 1$
D) $\frac { ( x + 5 ) ^ { 2 } } { 25 } + \frac { ( y + 4 ) ^ { 2 } } { 24 } = 1$

Question 58

Solve the problem.
A bridge is built in the shape of a semielliptical arch. It has a span of 102 feet. The height of the arch 25 feet from the center is to be 11 feet. Find the height of the arch at its center.

A) 25.6 ft
B) 22.44 ft
C) 12.62 ft
D) 11.35 ft

Question 59

Match the equation to the graph.
$16 x^{2}=9 y^{2}+144$

A)

B)

C)

D)

Question 60

Solve the problem.
A hall 130 feet in length was designed as a whispering gallery. If the ceiling is 25 feet high at the center, how far
from the center are the foci located?

Question 61

Find the asymptotes of the hyperbola.
A satellite following the hyperbolic path shown in the picture turns rapidly at (0, 4) and then moves closer and closer to the line y = 125 x as it gets farther from the tracking station at the origin. Find the equation that
Describes the path of the rocket if the center of the hyperbola is at (0, 0).
(0, 4)
Y = 125 x A) $\frac { y ^ { 2 } } { \frac { 25 } { 9 } } - \frac { x ^ { 2 } } { 16 } = 1$
B) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { \left( \frac { 36 } { 5 } \right) ^ { 2 } } = 1$
C) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { \frac { 25 } { 9 } } = 1$
D) $\frac { x ^ { 2 } } { \left( \frac { 36 } { 5 } \right) ^ { 2 } } - \frac { y ^ { 2 } } { 16 } = 1$

Question 62

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

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 63

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

A)

B)

C)

D)