Deck 11: Conic Sections

Question 1

Name the conic.

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

Answer 1

circle

Question 2

Graph the equation.

- $y = 4 ( x + 1 ) ^ { 2 } + 5$

A)
B)
C)
D)

Answer 2

Question 3

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $x=y^{2}-10 y+30$

A)
B)
C)
D)

Answer 3

Question 4

Graph the equation.

- $x = - ( y + 3 ) ^ { 2 } + 3$

A)
B)
C)
D)

Question 5

Name the conic.

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

Question 6

Graph the equation.

- $x = ( y + 6 ) ^ { 2 } + 2$

A)
B)
C)
D)

Question 7

Write the equation in the form $\mathbf { y = a ( x - h )} \mathbf {^ { 2 } + k.}$

- $y = x ^ { 2 } + 2 x - 7$

A) $y = ( x - 1 ) ^ { 2 } - 6$
B) $y = ( x + 1 ) ^ { 2 } - 8$
C) $y = ( x + 1 ) ^ { 2 } - 6$
D) $y = ( x - 1 ) ^ { 2 } - 8$

Question 8

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $y = - 3 x ^ { 2 } + 18 x - 31$

A)
B)
C)
D)

Question 9

Name the conic.

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

Question 10

Determine whether the graph of the quadratic function opens up or down.

- $f ( x ) = x ^ { 2 } + 8 x - 2$

A)down
B)up

Question 11

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $x = \frac { 1 } { 2 } y ^ { 2 } - 4 y + 9$

A)
B)
C)
D)

Question 12

Name the conic.

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

Question 13

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $x=-y^{2}-6 y-3$

A)
B)
C)
D)

Question 14

Graph the equation.

- $y = ( x - 6 ) ^ { 2 } - 5$

A)
B)
C)
D)

Question 15

Determine whether the graph of the quadratic function opens up or down.

- $f ( x ) = - 8 x ^ { 2 } + 9 x + 1$

A)down
B)up

Question 16

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $y = - 4 x ^ { 2 } - 32 x - 66$

A)
B)
C)
D)

Question 17

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $y = x ^ { 2 } + 4 x - 5$

A)
B)
C)
D)

Question 18

Graph the equation.

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

A)
B)
C)
D)

Question 19

Graph the equation.

- $x = - 2 ( y + 4 ) ^ { 2 } - 1$

A)
B)
C)
D)

Question 20

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $y = - x ^ { 2 } - 6 x - 8$

A)
B)
C)
D)

Question 21

Write the equation of the circle with the given center and radius.

-Center (1, 0), radius 4

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

Question 22

Determine the midpoint of the line segment between the pair of points.

-(3, -7)and (8, -3)

A)(11, -10)
B)(-5, -4)
C) $\left( \frac { 11 } { 2 } , - 5 \right)$
D) $\left( - \frac { 5 } { 2 } , - 2 \right)$

Question 23

Determine the distance between the pair of points.

-(2, -3)and (6, -1)

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

Question 24

Determine the distance between the pair of points.

-(0, 0)and (-10, -8)

A)164
B) $3 \sqrt { 2 }$
C) $2 \sqrt { 41 }$
D)-18

Question 25

Determine the distance between the pair of points.

-(-7, -7)and (5, 3)

A) $44 \sqrt { 11 }$
B)2
C)44
D) $2 \sqrt { 61 }$

Question 26

Determine the distance between the pair of points.

- $( 3 \sqrt { 6 } , 2 ) \text { and } ( 5 \sqrt { 6 } , 7 )$

A)6
B) $\frac { 49 } { 2 }$
C)7
D)49

Question 27

Determine the distance between the pair of points.

-(2, 5)and (-6, -6)

A)88
B) $\sqrt { 185 }$
C) $\sqrt { 57 }$
D)-3

Question 28

Write the equation of the circle with the given center and radius.

-Center (-10, 8), radiuss $\sqrt { 5 }$

A) $( x - 8 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 25$
B) $( x + 10 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 5$
C) $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = 25$
D) $( x - 10 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 5$

Question 29

Write the equation of the circle with the given center and radius.

-Center (0, 0),radiuss $2 \sqrt { 2 }$

A) $x ^ { 2 } + y ^ { 2 } = 8$
B) $x ^ { 2 } + y ^ { 2 } = 64$
C) $x ^ { 2 } + y ^ { 2 } = 2 \sqrt { 2 }$
D) $x ^ { 2 } + y ^ { 2 } = 4$

Question 30

Write the equation in the form $\mathbf {y = a ( x - h ) ^ { 2 } + k ~or ~ x = a ( y - k ) ^ { 2 } + h}$ h a nd then graph the equation.

- $x = 2 y ^ { 2 } + 12 y + 17$

A)
B)
C)
D)

Question 31

Graph the equation.

- $x ^ { 2 } + y ^ { 2 } = 9$

A)
B)

Question 32

Determine the midpoint of the line segment between the pair of points.

- $( 9 \sqrt { 5 } , 6 \sqrt { 5 } ) \text { and } ( 14 \sqrt { 5 } , 11 \sqrt { 5 } )$

A) $\left( \frac { 5 \sqrt { 5 } } { 2 } , \frac { 5 \sqrt { 5 } } { 2 } \right)$
B) $( 23 \sqrt { 5 } , 17 \sqrt { 5 } )$
C) $\left( \frac { - 5 \sqrt { 5 } } { 2 } , \frac { - 5 \sqrt { 5 } } { 2 } \right)$
D) $\left( \frac { 23 \sqrt { 5 } } { 2 } , \frac { 17 \sqrt { 5 } } { 2 } \right)$

Question 33

Determine the distance between the pair of points.
(-4, 2)and (-16, 7)

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

Question 34

Determine the midpoint of the line segment between the pair of points.
(6, 1)and (8, 5)

A)(- 1, - 2)
B)(14, 6)
C)(-2, -4)
D)(7, 3)

Question 35

Determine the distance between the pair of points.

-(0, -2)and (5, -2)

A)5
B)2
C)25
D) $\sqrt { 29 }$

Question 36

Determine the midpoint of the line segment between the pair of points.

- $\left( - \frac { 8 } { 5 } , - \frac { 3 } { 2 } \right) \text { and } \left( - \frac { 7 } { 5 } , - \frac { 5 } { 2 } \right)$

A) $\left( - \frac { 1 } { 10 } , \frac { 1 } { 2 } \right)$
B) $\left( \frac { 1 } { 10 } , - \frac { 1 } { 2 } \right)$
C) $\left( - \frac { 3 } { 2 } , - 2 \right)$
D)(- 3, - 4)

Question 37

Determine the distance between the pair of points.

-(1, -2)and (-1, -6)

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

Question 38

Write the equation of the circle with the given center and radius.

-Center (7, 6), radius 5

A) $( x + 6 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 5$
B) $( x - 7 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 25$
C) $( x + 7 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 25$
D) $( x - 6 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 5$

Question 39

Write the equation of the circle with the given center and radius.

-Center (0, 0),radius 3

A) $x ^ { 2 } - y ^ { 2 } = 3$
B) $x ^ { 2 } + y ^ { 2 } = 6$
C) $x ^ { 2 } + y ^ { 2 } = 9$
D) $x ^ { 2 } + y ^ { 2 } = 3$

Question 40

Write the equation of the circle with the given center and radius.

-Center (0, -10), radius 5

A) $x ^ { 2 } + ( y + 10 ) ^ { 2 } = 25$
B) $( x + 10 ) ^ { 2 } + y ^ { 2 } = 25$
C) $x ^ { 2 } + ( y - 10 ) ^ { 2 } = 5$
D) $( x - 10 ) ^ { 2 } + y ^ { 2 } = 25$

Question 41

Graph the equation.

- $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 1 } = 1$

A)
B)
C)
D)

Question 42

Graph the equation.

- $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 9$

A)
B)
C)
D)

Question 43

Graph the equation.

- $x ^ { 2 } + 4 y ^ { 2 } = 4$

A)
B)
C)
D)

Question 44

Write the equation of the circle. Assume the radius is a whole number.

-

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

Question 45

Use the method of completing the square to write the equation in standard form. Then graph the equation.

- $x ^ { 2 } + y ^ { 2 } + 4 x + 4 y + 4 = 0$

A)
B)
C)
D)

Question 46

Write the equation of the circle with the given center and radius.

- $\text { Center } ( 0 , - 8 ) , \quad \text { radius } \sqrt { 17 }$

A) $( x + 8 ) ^ { 2 } + y ^ { 2 } = 289$
B) $( x - 8 ) ^ { 2 } + y ^ { 2 } = 289$
C) $x ^ { 2 } + ( y - 8 ) ^ { 2 } = 17$
D) $x ^ { 2 } + ( y + 8 ) ^ { 2 } = 17$

Question 47

Use the method of completing the square to write the equation in standard form. Then graph the equation.

- $x ^ { 2 } + y ^ { 2 } - 8 x - 4 y + 4 = 0$

A)
B)
C)
D)

Question 48

Graph the equation.

- $( x - 5 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$

A)
B)
C)
D)

Question 49

Graph the equation.

- $( x - 3 ) ^ { 2 } + y ^ { 2 } = 4$

A)
B)
C)
D)

Question 50

Graph the equation.

- $16 x ^ { 2 } + 9 y ^ { 2 } = 144$

A)
B)
C)
D)

Question 51

Graph the equation.

- $4 x ^ { 2 } + 9 y ^ { 2 } = 36$

A)
B)
C)
D)

Question 52

Graph the equation.

- $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 16 } = 1$

A)
B)
C)
D)

Question 53

Graph the equation.

- $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$

A)
B)
C)
D)

Question 54

Graph the equation.

- $( x + 5 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$

A)
B)
C)
D)

Question 55

Graph the equation.

- $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 16$

A)
B)
C)
D)

Question 56

Graph the equation.

- $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

A)
B)
C)
D)

Question 57

Write the equation of the circle. Assume the radius is a whole number.

-

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

Question 58

Graph the equation.

- $49 x ^ { 2 } + y ^ { 2 } = 49$

A)
B)
C)
D)

Question 59

Write the equation of the circle. Assume the radius is a whole number.

-

A) $x ^ { 2 } + ( y - 7 ) ^ { 2 } = 2$
B) $( x + 7 ) ^ { 2 } + y ^ { 2 } = 4$
C) $x ^ { 2 } + ( y + 7 ) ^ { 2 } = 2$
D) $( x - 7 ) ^ { 2 } + y ^ { 2 } = 4$

Question 60

Find the equation of the ellipse satisfying the given conditions.

-(4, 0), (-4, 0), (0, 3), (0, -3)are the endpoints of the major and minor axes.

A) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$

Question 61

Graph the equation.

- $16 ( x + 1 ) ^ { 2 } + 9 ( y - 1 ) ^ { 2 } = 144$

A)
B)
C)
D)

Question 62

Graph the equation.

- $9 ( x - 2 ) ^ { 2 } + 16 ( y + 2 ) ^ { 2 } = 144$

A)
B)
C)
D)

Question 63

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.

- $25 y^{2}-4 x^{2}=100$

A) $y = \pm \frac { 5 } { 2 } x$


B) $y = \pm \frac { 5 } { 2 } x$


C) $y = \pm \frac { 2 } { 5 } x$


D) $y = \pm \frac { 2 } { 5 } x$

Question 64

Find the equation of the ellipse satisfying the given conditions.

-(0, 6), (0, -6), (3, 0), (-3, 0)are the endpoints of the major and minor axes.

A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 144 } = 1$
C) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 36 } = 1$

Question 65

Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 34 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use
This road. They are both 8 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an overall height of
11 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A)Neither Truck 1 nor Truck 2 can pass under the bridge.
B)Truck 1 can pass under the bridge, but Truck 2 cannot.
C)Truck 2 can pass under the bridge, but Truck 1 cannot.
D)Both Truck 1 and Truck 2 can pass under the bridge.

Question 66

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.

- $25 x^{2}-4 y^{2}=100$

A) $y = \pm \frac { 5 } { 2 } x$


B) $y = \pm \frac { 5 } { 2 } x$


C) $y = \pm \frac { 2 } { 5 } x$


D) $y = \pm \frac { 2 } { 5 } x$

Question 67

Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and the height of the arch over the center of the roadway is 14 feet. Two trucks plan to use
This road. They are both 12 feet wide. Truck 1 has an overall height of 13 feet and Truck 2 has an overall height
Of 14 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A)Neither Truck 1 nor Truck 2 can pass under the bridge.
B)Truck 1 can pass under the bridge, but Truck 2 cannot.
C)Truck 2 can pass under the bridge, but Truck 1 cannot.
D)Both Truck 1 and Truck 2 can pass under the bridge.

Question 68

Solve the problem.
An arch for a bridge over a highway is in the form of a semi-ellipse. The top of the arch is 35 feet above ground. What should the span of the bridge be, rounded to the nearest hundredth of a foot, if the height 26 feet from the
Center is to be 12 feet above ground?

A)27.68 ft
B)151.67 ft
C)55.36 ft
D)35.85 ft

Question 69

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.

- $25 x^{2}=4 y^{2}+100$

A) $y = \pm \frac { 5 } { 2 } x$


B) $y = \pm \frac { 2 } { 5 } x$


C) $y = \pm \frac { 5 } { 2 } x$


D) $y = \pm \frac { 2 } { 5 } x$

Question 70

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.

- $16 y ^ { 2 } = 4 x ^ { 2 } + 64$

A) $y = \pm \frac { 1 } { 2 } x$


B) $y = \pm \frac { 1 } { 2 } x$


C) $y = \pm 2 x$


D) $y = \pm 2 x$

Question 71

Determine the equations of the asymptotes for the equation.

- $y ^ { 2 } - x ^ { 2 } = 16$

A) $y = \pm \frac { 1 } { 4 } x$
B) $y = \pm 4 x$
C) $y = \pm x$
D) $y = \pm \frac { 1 } { 16 } x$

Question 72

Solve the problem.

-Find the equation of the ellipse, if (-7, -3)and (5, -3)are the endpoints of the major axis and (-1, -6)and (-1, 0) are the endpoints of the minor axis.

A) $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$
B) $\frac { ( x - 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$
C) $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y + 3 ) ^ { 2 } } { 9 } = 1$
D) $\frac { ( x + 1 ) ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$

Question 73

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.

- $\frac { y ^ { 2 } } { 4 } - \frac { x ^ { 2 } } { 16 } = 1$

A) $y= \pm 2 x$


B) $y = \pm 2 x$


C) $y = \pm \frac { 1 } { 2 } x$


D) $y = \pm \frac { 1 } { 2 } x$

Question 74

Graph the equation.

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

A)
B)
C)
D)

Question 75

Determine the equations of the asymptotes for the equation.

- $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$

A) $y = \pm \frac { 16 } { 25 } x$
B) $y = \pm \frac { 5 } { 4 } x$
C) $y = \pm \frac { 25 } { 16 } x$
D) $y = \pm \frac { 4 } { 5 } x$

Question 76

Solve the problem.
The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use
This road. They are both 8 feet wide. Truck 1 has an overall height of 11 feet and Truck 2 has an overall height of
10 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A)Both Truck 1 and Truck 2 can pass under the bridge.
B)Truck 1 can pass under the bridge, but Truck 2 cannot.
C)Truck 2 can pass under the bridge, but Truck 1 cannot.
D)Neither Truck 1 nor Truck 2 can pass under the bridge.

Question 77

Write the equation in standard form (if necessary)and determine the equations of the asymptotes. Then graph the
equation.

- $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$

A) $y = \pm \frac { 2 } { 3 } x$

B) $y = \pm \frac { 3 } { 2 } x$

C) $y = \pm \frac { 3 } { 2 } x$

D) $y = \pm \frac { 2 } { 3 } x$

Question 78

Graph the equation.

- $\frac { ( x - 2 ) ^ { 2 } } { 9 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$

A)
B)
C)
D)

Question 79

Solve the problem.
A bridge is built in the shape of a semi-elliptical arch. It has a span of 118 feet. The height of the arch 30 feet from the center is to be 12 feet. Find the height of the arch at its center rounded to the nearest hundredth of a
Foot.

A)12.41 ft
B)23.6 ft
C)13.94 ft
D)30.64 ft

Question 80

Write the following equation in standard form. Determine the center of the ellipse.

- $16 x ^ { 2 } + 64 x + 9 y ^ { 2 } - 54 y + 1 = 0$

A)(-1, 3)
B)(-2, 3)
C)(3, -2)
D)(2, 3)