Deck 10: The Conic Sections

Question 1

Find the standard form of the equation of the following conic section.
center $( - 6 , - 1 ) ; r = 11$

A) $( x + 6 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 121$
B) $( x - 1 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 11$
C) $( x + 1 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 11$
D) $( x - 6 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 121$

Answer 1

A

Question 2

Find the value of the unknown coordinate so that the distance between the points is as given.
$( 3,4 )$ and $( x , 7 )$ ; distance is $3.61$

A) $x = 6 , x = 5$
B) $x = 1 , x = 5$
C) $x = 1 , x = 13$
D) $x = - 6 , x = 5$

Answer 2

B

Question 3

Give the center and radius of the circle. Then sketch its graph.
$$( x + 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 25$$

A) center $( 4,2 ) , \mathrm { r } = 5$

B) center $( - 4 , - 2 ) , r = 5$

C) center $( 4 , - 2 ) , r = 5$

D) center $( - 4,2 ) , r = 5$

Answer 3

B

Question 4

Find the standard form of the equation of the following conic section.
center $( 5,0 ) ; r = 2 \sqrt { 2 }$

A) $( x - 5 ) ^ { 2 } + y ^ { 2 } = 2 \sqrt { 2 }$
B) $( x - 5 ) ^ { 2 } + y ^ { 2 } = 64$
C) $( x - 5 ) ^ { 2 } + y ^ { 2 } = 8$
D) $( x + 5 ) ^ { 2 } + y ^ { 2 } = 8$

Question 5

Give the center and radius of the circle. Then sketch its graph.
$$( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 9$$
A) center $( - 1 , - 2 ) , r = 3$

B) center $( 1 , - 2 ) , \mathrm { r } = 3$

C) center $( - 1,2 ) , \mathrm { r } = 3$

D) center $( 1,2 ) , r = 3$

Question 6

Find the standard form of the equation of the following conic section.
center $( - 4 , - 1 ) ; r = \sqrt { 3 }$

A) $( x - 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 9$
B) $( x - 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$
C) $( x + 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$
D) $( x + 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$

Question 7

Find the distance between the pair of points. Give an exact answer.
(4, 4)and (-1, 16)

A)14 units
B)13 units
C)26 units
D)169 units

Question 8

Find the distance between the pair of points. Give an exact answer.
$( 4,4 )$ and $( - 5 , - 7 )$

A) $2 \sqrt { 10 }$ units
B) 99 units
C) 202 units
D) $\sqrt { 202 }$ units

Question 9

Give the center and radius of the circle. Then sketch its graph.
$$x ^ { 2 } + y ^ { 2 } = 16$$

A) center $( 1,1 ) , r = 16$

B) center $( 0,0 ) , r = 4$

C) center $( 0,0 ) , r = 16$

D) center $( 1,1 ) , r = 4$

Question 10

Give the center and radius of the circle. Then sketch its graph.
$$( x + 3 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 16$$
A) center B) center \(( 3,4 ) , \mathrm { r } = 4">( - 3 , - 4 ) , \mathrm { r } = 4\)<img src="https://d2lvgg3v3hfg70.cloudfront.net/TB6914/11ecb33d_8774_ac61_a9b7_7d2e48059aeb_TB6914_00.jpg" alt=" Give the center and radius of the circle. Then sketch its graph. ( x + 3 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 16 A) center ( - 3 , - 4 ) , \mathrm { r } = 4\ ) B) center ( 3,4 ) , \mathrm { r } = 4 11 ecb33d_8d39_9252_a9b7_155027a344e9_TB6914_00 C) center ( - 3,4 ) , r = 4 D) center ( 3 , - 4 ) , r = 4 " class="answers-bank-image d-block" loading="lazy" >B) center \(( 3,4 ) , \mathrm { r } = 4 11
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C) center $( - 3,4 ) , r = 4$

D) center $( 3 , - 4 ) , r = 4$

Question 11

Find the distance between the pair of points. Give an exact answer.
$( - 5 , - 1 )$ and $( 2 , - 2 )$

A) 48 units
B) $5 \sqrt { 2 }$ units
C) $48 \sqrt { 3 }$ units
D) 8 units

Question 12

Find the distance between the pair of points. Give an exact answer.
$( 2 , - 5 )$ and $( 4 , - 1 )$

A) $12 \sqrt { 3 }$ units
B) 2 units
C) 12 units
D) $2 \sqrt { 5 }$ units

Question 13

Find the standard form of the equation of the following conic section.
center $\left( 0 , \frac { 9 } { 8 } \right) ; r = \frac { 1 } { 4 }$

A) $x ^ { 2 } + \left( y + \frac { 9 } { 8 } \right) ^ { 2 } = \frac { 1 } { 4 }$
B) $x ^ { 2 } + \left( y + \frac { 9 } { 8 } \right) ^ { 2 } = \frac { 1 } { 16 }$
C) $x ^ { 2 } + \left( y - \frac { 9 } { 8 } \right) ^ { 2 } = \frac { 1 } { 4 }$
D) $x ^ { 2 } + \left( y - \frac { 9 } { 8 } \right) ^ { 2 } = \frac { 1 } { 16 }$

Question 14

Find the value of the unknown coordinate so that the distance between the points is as given.
$( 1.5 , - 2 )$ and $( 0 , y )$ ; distance is $2.5$

A) $\mathrm { y } = - 4.5 , \mathrm { y } = 0.5$
B) $\mathrm { y } = 0 , \mathrm { y } = - 0.5$
C) $\mathrm { y } = 0 , \mathrm { y } = - 4$
D) $y = 0 , y = 3.5$

Question 15

Find the value of the unknown coordinate so that the distance between the points is as given.
$( 3,6.25 )$ and $( x , - 1.75 )$ ; distance is 10

A) $x = - 3 , x = 9$
B) $x = - 2 , x = 10$
C) $x = 0 , x = 12$
D) $x = 1 , x = 13$

Question 16

Find the distance between the pair of points. Round to the nearest thousandth.
(-4, -3.9)and (-9, 9.3)

A)18.3
B)14.115
C)199.24
D)14.077

Question 17

Find the distance between the pair of points. Give an exact answer.
$( - 3 , - 7 )$ and $( 3,2 )$

A) 45 units
B) $45 \sqrt { 5 }$ units
C) $3 \sqrt { 13 }$ units
D) 3 units

Question 18

Find the value of the unknown coordinate so that the distance between the points is as given.
$( 1,4 )$ and $( 6 , y )$ ; distance is 13

A) $y = 148 , y = - 190$
B) $y = 12 , y = - 4$
C) $y = 16 , y = - 8$
D) $y = 17.93 , y = - 9.93$

Question 19

Find the standard form of the equation of the following conic section.
center $( - 1.3,0 ) ; r = 3$

A) $( x + 1.3 ) ^ { 2 } + y ^ { 2 } = 9$
B) $( x - 1.3 ) ^ { 2 } + y ^ { 2 } = 3$
C) $( x + 1.3 ) ^ { 2 } + y ^ { 2 } = 3$
D) $( x - 1.3 ) ^ { 2 } + y ^ { 2 } = 9$

Question 20

Find the distance between the pair of points. Round to the nearest thousandth.
$\left( \frac { 1 } { 2 } , \frac { 1 } { 7 } \right)$ and $\left( \frac { 3 } { 4 } , \frac { 8 } { 7 } \right)$

A) $0.250$
B) 4
C) $1.031$
D) $0.970$

Question 21

Graph the parabola and label the vertex. Find the x-intercept.
$$x = \frac { 3 } { 4 } y ^ { 2 }$$
A) vertex $( 0,0 ) , x$ -intercept $( 0,0 )$

B) vertex $( 0,0 ) , x$ -intercept $( 0,0 )$

C) vertex $( 0,0 ) , x$ -intercept $( 0,0 )$

D) vertex $( 0,0 ) , x$ -intercept $( 0,0 )$

Question 22

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } + 4 x - 96 = 0$$

A) $( x + 2 ) ^ { 2 } + y ^ { 2 } = 100$
center $( - 2,0 ) , \mathrm { r } = 10$
B) $( x + 2 ) ^ { 2 } + y ^ { 2 } = 100$
center $( 2,0 ) , r = 10$
C) $x ^ { 2 } + ( y + 2 ) ^ { 2 } = 100$
center $( 0 , - 2 ) , \mathrm { r } = 10$
D) $( x - 2 ) ^ { 2 } + y ^ { 2 } = 100$
center $( 2,0 ) , r = 10$

Question 23

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } - 12 x - 12 y + 59 = 0$$

A) $( x + 6 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 13$
center $( - 6 , - 6 ) , r = \sqrt { 13 }$
B) $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 13$
center $( 6,6 ) , r = \sqrt { 13 }$
C) $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 13$
center $( - 6 , - 6 ) , r = \sqrt { 13 }$
D) $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 13$
center $( 6,6 ) , r = 13$

Question 24

Give the center and radius of the circle. Then sketch its graph.
$$\left( x - \frac { 2 } { 5 } \right) ^ { 2 } + ( y + 5 ) ^ { 2 } = 25$$
A) center $\left( - \frac { 2 } { 5 } , - 5 \right) , \mathrm { r } = 5$

B) center $\left( \frac { 2 } { 5 } , - 5 \right) , \mathrm { r } = 5$

C) center $\left( \frac { 2 } { 5 } , 5 \right) , \mathrm { r } = 5$

D) center $\left( - \frac { 2 } { 5 } , 5 \right) , \mathrm { r } = 5$

Question 25

Use the following information to solve the problem. An airport is located at point O. A short-range radar tower is located
at point R. The maximum range at which the radar can detect a plane is 4 miles from point R.
Assume that R is 2 miles east of O and 7 miles north of O. In other words, R is located at the point (2, 7). An airplane is flying parallel to and 1 miles east of the north axis. (In other words, the plane is flying along the path
X = 1.)What is the greatest distance north of the airport at which the plane can still be detected by the radar
Tower at R? Round your answer to the nearest tenth of a mile.

A)10.9 miles
B)10 miles
C)3)1 miles
D)9)2 miles

Question 26

Graph the parabola and label the vertex. Find the y-intercept.
$y=-5 x^{2}$
A) vertex $( 0,0 ) , y$ -intercept $( 0,0 )$

B) vertex $( 0,0 )$ , y-intercept $( 0,0 )$

C) vertex $( 0,0 ) , y$ -intercept $( 0,0 )$

D) vertex $( 0,0 )$ , y-intercept $( 0,0 )$

Question 27

Give the center and radius of the circle. Then sketch its graph.
$$( x - 2 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 25$$
A) center $( 2,5 ) , r = 5$

B) center $( - 2,5 ) , \mathrm { r } = 5$

C) center $( 2 , - 5 ) , r = 5$

D) center $( - 2 , - 5 ) , r = 5$

Question 28

Graph the parabola and label the vertex. Find the x-intercept.
$$x = \frac { 1 } { 4 } y ^ { 2 } + 5$$
A) vertex $( 5,0 ) , x$ -intercept $( 5,0 )$

B) vertex $( - 5,0 ) , x$ -intercept $( - 5,0 )$

C) vertex $( - 5,0 ) , x$ -intercept $( - 5,0 )$

D) vertex $( 5,0 ) , x$ -intercept $( 5,0 )$

Question 29

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } + 12 x - 6 y - 164 = 0$$

A) $( x - 12 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 16$
center $( 12 , - 6 ) , r = 4$
B) $( x - 12 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 16$
center $( - 12,6 ) , r = 4$
C) $( x + 12 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 16$
center $( - 12,6 ) , r = 4$
D) $( x + 12 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 16$
center $( 12 , - 6 ) , \mathrm { r } = 4$

Question 30

Graph the parabola and label the vertex. Find the y-intercept.
$y=x^{2}+8$
A) vertex $( 0 , - 8 ) , y$ -intercept $( 0 , - 8 )$

B) vertex $( 0 , \quad ) , y$ -intercept $( 0 , \quad )$

C) vertex $( 0 , \quad ) , y$ -intercept $( 0 , \quad )$

D) vertex $( 0 , - 8 ) , y$ -intercept $( 0 , - 8 )$

Question 31

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } - 16 x + 39 = 0$$

A) $( x - 8 ) ^ { 2 } + y ^ { 2 } = 25$
center $( - 8,0 ) , r = 5$
B) $x ^ { 2 } + ( y - 8 ) ^ { 2 } = 25$
center $( 0,8 ) , r = 5$
C) $( x - 8 ) ^ { 2 } + y ^ { 2 } = 25$
center $( 8,0 ) , \mathrm { r } = 5$
D) $( x + 8 ) ^ { 2 } + y ^ { 2 } = 25$
center $( - 8,0 ) , r = 5$

Question 32

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } - 6 x - 16 y + 73 = 49$$

A) ( x + 3 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 49 center \(( - 3 , - 8 ) , r = 49B)\(( x - 3 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 49center \(( 3,8 ) , { r } = 7C) \(( x - 8 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 49 center \(( 8,3 ) , r = 7D) \(( x - 3 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 49 center $( 3,8 ) , r = 49$

Question 33

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } + 6 x - 8 y - 56 = 0$$

A) ( x + 3 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 81 center \(( - 3,4 ) , r = 9B) \(( x - 3 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 81 center \(( 3 , - 4 ) , r = 9C) \(( x - 4 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 81center \(( 4 , - 3 ) , \ { r } = 9
D) ( x + 3 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 81 center \(( - 3,4 ) , r = 81

Question 34

Graph the parabola and label the vertex. Find the y-intercept.
$$y = - 4 \left( x - \frac { 13 } { 2 } \right) ^ { 2 } - 3$$
A) vertex $\left( \frac { 13 } { 2 } , - 3 \right) , y$ -intercept $( 0,172 )$

B) vertex $\left( \frac { 13 } { 2 } , - 3 \right)$ , y-intercept $( 0 , - 172 )$

C) vertex $\left( \frac { 13 } { 2 } , 3 \right) , y$ -intercept $( 0 , - 172 )$

D) vertex $\left( - \frac { 13 } { 2 } , - 3 \right)$ , y-intercept $( 0 , - 172 )$

Question 35

Use the following information to solve the problem. An airport is located at point O. A short-range radar tower is located
at point R. The maximum range at which the radar can detect a plane is 4 miles from point R.
A Ferris wheel has a radius r of 25.8 feet. The height of the tower t is 49.7 feet. The distance d from the origin to the base is 43.9 feet. Find the standard form equation of the circle represented by the Ferris wheel.

A) $( x + 43.9 ) ^ { 2 } + ( y + 49.7 ) ^ { 2 } = 25.8$
B) $( x + 43.9 ) ^ { 2 } + ( y + 49.7 ) ^ { 2 } = 665.64$
C) $( x - 43.9 ) ^ { 2 } + ( y - 49.7 ) ^ { 2 } = 25.8$
D) $( x - 43.9 ) ^ { 2 } + ( y - 49.7 ) ^ { 2 } = 665.64$

Question 36

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } + 14 y + 40 = 0$$

A) $( x + 7 ) ^ { 2 } + y ^ { 2 } = 9$
center $( - 7,0 ) , \mathrm { r } = 3$
B) $x ^ { 2 } + ( y + 7 ) ^ { 2 } = 9$
center $( 0 , - 7 ) , r = 3$
C) $x ^ { 2 } + ( y - 7 ) ^ { 2 } = 9$
center $( 0,7 ) , \mathrm { r } = 3$
D) $x ^ { 2 } + ( y + 7 ) ^ { 2 } = 9$
center $( 0,7 ) , r = 3$

Question 37

Graph the parabola and label the vertex. Find the y-intercept.
$$y = 4 ( x - 8 ) ^ { 2 } - \frac { 11 } { 2 }$$
A) vertex $\left( 8 , - \frac { 11 } { 2 } \right) , y$ -intercept $( 0 , - 250.5 )$

B) vertex $\left( 8 , - \frac { 11 } { 2 } \right) , y$ -intercept $( 0,250.5 )$

C) vertex $\left( - 8 , - \frac { 11 } { 2 } \right) , y$ -intercept $( 0,250.5 )$

D) vertex $\left( 8 , \frac { 11 } { 2 } \right) , \mathrm { y }$ -intercept $( 0,261.5 )$

Question 38

Use the following information to solve the problem. An airport is located at point O. A short-range radar tower is located
at point R. The maximum range at which the radar can detect a plane is 4 miles from point R.
Assume that R is 7 miles east of O and 11 miles north of O. In other words, R is located at the point (7, 11). An airplane is flying parallel to and 9 miles east of the north axis. (In other words, the plane is flying along the path
X = 9.)What is the shortest distance north of the airport at which the plane can still be detected by the radar
Tower at R? Round your answer to the nearest tenth of a mile.

A)24.8 miles
B)14.5 miles
C)7)5 miles
D)25.5 miles

Question 39

Rewrite the equation in standard form. Find the center and radius of the circle.
$$x ^ { 2 } + y ^ { 2 } - 12 y + 20 = 0$$

A) $x ^ { 2 } + ( y + 6 ) ^ { 2 } = 16$
center $( 0 , - 6 ) , \mathrm { r } = 4$
B) $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 16$
center $( 0,6 ) , \mathrm { r } = 4$
C) $( x - 6 ) ^ { 2 } + y ^ { 2 } = 16$
center $( 6,0 ) , \mathrm { r } = 4$
D) $x ^ { 2 } + ( y - 6 ) ^ { 2 } = 16$
center $( 0 , - 6 ) , \mathrm { r } = 4$

Question 40

Graph the parabola and label the vertex. Find the y-intercept.
$$y = \frac { 1 } { 2 } x ^ { 2 } + 1$$
A) vertex (0, ), y-intercept $( 0 , \quad )$

B) vertex $( 0 , \quad ) , y$ -intercept $( 0 , \quad )$

C) vertex $( 0 , - 1 )$ , y-intercept $( 0 , - 1 )$

D) vertex $( 0 , - 1 )$ , $y$ -intercept $( 0 , - 1 )$
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Question 41

Rewrite the equation in standard form. Determine whether the parabola is horizontal or vertical, the direction it opens,
and the vertex.
$$y = x ^ { 2 } - 14 x + 39$$

A) $y = ( x + 7 ) ^ { 2 } + 10$
vertical, opens upward, vertex $( - 7,10 )$
B) $y = ( x + 10 ) ^ { 2 } + 7$
vertical, opens upward, vertex $( - 10,7 )$
C) $y = ( x - 10 ) ^ { 2 } - 7$
vertical, opens upward, vertex $( 10 , - 7 )$
D) $y = ( x - 7 ) ^ { 2 } - 10$
vertical, opens upward, vertex $( 7 , - 10 )$

Question 42

Rewrite the equation in standard form. Determine whether the parabola is horizontal or vertical, the direction it opens,
and the vertex.
$$y = - 3 x ^ { 2 } + 72 x - 441$$

A) $y = ( x + 12 ) ^ { 2 } - 9$
vertical, opens downward, vertex $( - 12 , - 9 )$
B) $y = ( x - 12 ) ^ { 2 } - 9$
vertical, opens upward, vertex $( 12 , - 9 )$
C) $y = ( x + 12 ) ^ { 2 } - 9$
vertical, opens upward, vertex $( - 12 , - 9 )$
D) $y = ( x - 12 ) ^ { 2 } - 9$
vertical, opens downward, vertex $( 12 , - 9 )$

Question 43

Graph the ellipse. Label the intercepts.
$$\frac { x ^ { 2 } } { \frac { 9 } { 4 } } + \frac { y ^ { 2 } } { \frac { 25 } { 4 } } = 1$$

A) $\left( - \frac { 3 } { 2 } , 0 \right) , \left( \frac { 3 } { 2 } , 0 \right) , \left( 0 , - \frac { 5 } { 2 } \right) , \left( 0 , \frac { 5 } { 2 } \right)$

B) $\left( - \frac { 2 } { 3 } , 0 \right) , \left( \frac { 2 } { 3 } , 0 \right) , \left( 0 , - \frac { 2 } { 5 } \right) , \left( 0 , \frac { 2 } { 5 } \right)$

C) $\left( - \frac { 2 } { 5 } , 0 \right) , \left( \frac { 2 } { 5 } , 0 \right) , \left( 0 , - \frac { 2 } { 3 } \right) , \left( 0 , \frac { 2 } { 3 } \right)$

D) $\left( 0 , - \frac { 3 } { 2 } \right) , \left( 0 , \frac { 3 } { 2 } \right) , \left( - \frac { 5 } { 2 } , 0 \right) , \left( \frac { 5 } { 2 } , 0 \right)$

Question 44

Rewrite the equation in standard form. Determine whether the parabola is horizontal or vertical, the direction it opens,
and the vertex.
$$x = y ^ { 2 } + 14 y + 44$$

A) $x = ( y + 7 ) ^ { 2 } - 5$
horizontal, opens to the right, vertex $( - 5 , - 7 )$
B) $x = ( y + 7 ) ^ { 2 } - 5$
horizontal, opens to the right, vertex $( - 7 , - 5 )$
C) $x = ( y + 7 ) ^ { 2 } - 5$
horizontal, opens to the left, vertex $( - 5 , - 7 )$
D) $x = ( y + 5 ) ^ { 2 } - 7$
horizontal, opens to the left, vertex $( - 7 , - 5 )$

Question 45

Graph the ellipse and label the center.
$$\frac { ( x - 11 ) ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$$

A) $\mathrm { C } ( 11,0 )$

B) $\mathrm { C } ( - 11,0 )$

C) C $( 0 , - 11 )$

D) $\mathrm { C } ( 0,11 )$

Question 46

Graph the ellipse and label the center.
$$\frac { x ^ { 2 } } { 36 } + \frac { ( y - 10 ) ^ { 2 } } { 16 } = 1$$

A) $C ( 0,10 )$

B) $\mathrm { C } ( - 10,0 )$

C) $C ( 0 , - 10 )$

D) $\mathrm { C } ( 10,0 )$

Question 47

Graph the ellipse and label the center.
$$\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y - 9 ) ^ { 2 } } { 36 } = 1$$

A) $C ( - 2 , - 9 )$

B) $\mathrm { C } ( - 3 , - 6 )$

C) $\mathrm { C } ( 2,9 )$

D) $\mathrm { C } ( 3,6 )$

Question 48

Graph the ellipse. Label the intercepts.
$$45 x ^ { 2 } + y ^ { 2 } = 225$$

A) $( - \sqrt { 5 } , 0 ) , ( \sqrt { 5 } , 0 ) , ( 0 , - \sqrt { 15 } ) , ( 0 , \sqrt { 15 } )$

В) $( - \sqrt { 5 } , 0 ) , ( \sqrt { 5 } , 0 ) , ( 0 , - 15 ) , ( 0,15 )$

C) $( - 5,0 ) , ( 5,0 ) , ( 0 , - \sqrt { 15 } ) , ( 0 , \sqrt { 15 } )$

D) $( - 5,0 ) , ( 5,0 ) , ( 0 , - 15 ) , ( 0,15 )$

Question 49

Graph the parabola and label the vertex. Find the x-intercept.
$$x = - 2 ( y + 1 ) ^ { 2 } - 7$$
A) vertex $( - 7 , - 1 ) , x$ -intercept $( - 5,0 )$

B) vertex $( 7 , - 1 ) , x$ -intercept $( - 9,0 )$

C) vertex $( 7 , - 1 ) , x$ -intercept $( 9,0 )$

D) vertex $( - 7 , - 1 ) , x$ -intercept $( , 0 )$

Question 50

Graph the ellipse. Label the intercepts.
$$x ^ { 2 } + 4 y ^ { 2 } = 64$$

A) $( - 8,0 ) , ( 8,0 ) , ( 0 , - 2 ) , ( 0,2 )$

B) $( - 4,0 ) , ( 4,0 ) , ( 0 , - 8 ) , ( 0,8 )$

C) $( - 8,0 ) , ( 8,0 ) , ( 0 , - 4 ) , ( 0,4 )$

D) $( - 2,0 ) , ( 2,0 ) , ( 0 , - 8 ) , ( 0,8 )$

Question 51

Graph the ellipse and label the center.
$$\frac { x ^ { 2 } } { 36 } + \frac { ( y + 8 ) ^ { 2 } } { 100 } = 1$$

A) $\mathrm { C } ( - 8,0 )$

B) $\mathrm { C } ( 8,0 )$

C) $C ( 0,8 )$

D) $C ( 0 , - 8 )$

Question 52

Graph the ellipse. Label the intercepts.
$$16 x ^ { 2 } + y ^ { 2 } - 64 = 0$$

A) $( - 2,0 ) , ( 2,0 ) , ( 0 , - 4 ) , ( 0,4 )$

B) $( - 2,0 ) , ( 2,0 ) , ( 0 , - 8 ) , ( 0,8 )$

C) $( - 4,0 ) , ( 4,0 ) , ( 0 , - 2 ) , ( 0,2 )$

D) $( - 8,0 ) , ( 8,0 ) , ( 0 , - 2 ) , ( 0,2 )$

Question 53

Graph the ellipse. Label the intercepts.
$$\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 81 } = 1$$

A) $( - 2,0 ) , ( 2,0 ) , ( 0 , - 2 ) , ( 0,2 )$

B) $( - 9,0 ) , ( 9,0 ) , ( 0 , - 9 ) , ( 0,9 )$

C) $( - 2,0 ) , ( 2,0 ) , ( 0 , - 9 ) , ( 0,9 )$

D) $( - 9,0 ) , ( 9,0 ) , ( 0 , - 2 ) , ( 0,2 )$

Question 54

Solve.
Find an equation of the form $y = a x ^ { 2 }$ that describes the outline of a satellite dish such that the bottom of the dish passes through $( 0,0 )$ , the diameter of the dish is 20 inches, and the depth of the dish is 7 inches

A) $y = \frac { 7 } { 400 } x ^ { 2 }$
B) $y = \frac { 7 } { 20 } x ^ { 2 }$
C) $y = \frac { 7 } { 100 } x ^ { 2 }$
D) $y = \frac { 7 } { 10 } x ^ { 2 }$

Question 55

Graph the ellipse. Label the intercepts.
$$9 x ^ { 2 } + 16 y ^ { 2 } = 144$$

A) $( - 3,0 ) , ( 3,0 ) , ( 0 , - 4 ) , ( 0,4 )$

B) $( - 4,0 ) , ( 4,0 ) , ( 0 , - 3 ) , ( 0,3 )$

C) $( - 3,0 ) , ( 3,0 ) , ( 0 , - 4 ) , ( 0,4 )$

D) $( - 4,0 ) , ( 4,0 ) , ( 0 , - 3 ) , ( 0,3 )$

Question 56

Determine the center of the ellipse.
$$\frac { ( \mathrm { x } + 5 ) ^ { 2 } } { 9 } + \frac { ( \mathrm { y } - 5 ) ^ { 2 } } { 25 } = 1$$

A) (-5,-5)
B)(,5)
C) (,-5)
D) (-5,5)

Question 57

Solve.
The effective yield from a grove of miniature pear trees is described by the equation $\mathrm { E } = x ( 800 - x )$ , where $x$ is the number of pear trees per acre. What is the maximum effective yield? How many pear trees per acre should be planted to achieve the maximum yield?

A) Maximum yield $= 160,000$
number of trees per acre planted $= 800$
B) Maximum yield $= 160,000$
number of trees per acre planted $= 400$
C) Maximum yield $= 160,000$
number of trees per acre planted $= 200$
D) Maximum yield $= 40,000$
number of trees per acre planted $= 200$

Question 58

Graph the parabola and label the vertex. Find the x-intercept.
$$x = ( y - 5 ) ^ { 2 } + 8$$
A) vertex $( 8,5 ) , x$ -intercept $( 33,0 )$

B) vertex $( - 8 , - 5 ) , x$ -intercept $( 17,0 )$

C) vertex $( 8 , - 5 ) , x$ -intercept $( 33,0 )$

D) vertex $( - 8,5 ) , x$ -intercept $( 17,0 )$

Question 59

Graph the parabola and label the vertex. Find the x-intercept.
$$x = - y ^ { 2 } + 7$$
A) vertex $( , 0 ) , x$ -intercept $( , 0 )$

B) vertex $( - 7,0 ) , x$ -intercept $( - 7,0 )$

C) vertex $( , 0 ) , x$ -intercept $( , 0 )$

D) vertex $( - 7,0 ) , x$ -intercept $( - 7,0 )$

Question 60

Solve.
A specialty watch company's monthly profit equation is
$$P = - 2 x ^ { 2 } + 1000 x + 50,000 \text {, }$$
where $x$ is the number of watches manufactured. Find the maximum monthly profit and the number of watches must be produced each month to attain the maximum profit.

A) Maximum profit $= \$ 50,000$
number of watches produced $= 1000$
B) Maximum profit $= \$ 175,000$
number of watches produced $= 250$
C) Maximum profit $= \$ 175,000$
number of watches produced $= 500$
D) Maximum profit $= \$ 50,000$
number of watches produced $= 0$

Question 61

Graph the ellipse and label the center.
$$\frac { ( x + 2 ) ^ { 2 } } { 49 } + \frac { ( y - 10 ) ^ { 2 } } { 16 } = 1$$

A) $\mathrm { C } ( - 2 , - 10 )$

B) $\mathrm { C } ( 2 , - 10 )$

C) $\mathrm { C } ( 2,10 )$

D) $\mathrm { C } ( - 2,10 )$

Question 62

Graph the ellipse and label the center.
$$\frac { ( x + 4 ) ^ { 2 } } { 49 } + \frac { ( y + 11 ) ^ { 2 } } { 25 } = 1$$

A) $\mathrm { C } ( 4 , - 11 )$

B) $\mathrm { C } ( 4,11 )$

C) $\mathrm { C } ( - 4,11 )$

D) $\mathrm { C } ( - 4 , - 11 )$

Question 63

Graph the ellipse and label the center.
$$\frac { ( x - 11 ) ^ { 2 } } { 100 } + \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$$

A) $C ( 11 , - 4 )$

B) $\mathrm { C } ( - 11,4 )$

C) $\mathrm { C } ( 11,4 )$

D) $C ( - 11 , - 4 )$

Question 64

Graph the ellipse and label the center.
$$\frac { ( x + 4 ) ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$$

A) $\mathrm { C } ( 0,4 )$

B) $\mathrm { C } ( - 4,0 )$

C) $\mathrm { C } ( 0 , - 4 )$

D) $\mathrm { C } ( 4,0 )$