Free Printable Conic Sections Review

1.

The set of all points in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) in the plane is called _______.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

2.

Identify the type of conic section by inspection.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

3.

A conic section that has the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

4.

Identify the type of conic section.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

5.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

6.

Classify the conic section and its orientation is possible.

a)

Ellipse, Vertical major axis

b)

Hyperbola, Vertical tranverse axis

c)

Parabola, opens to the Right

d)

Parabola, opens to the Left

7.

A type of conic section which has the set of all points that are equidistant from a fixed point in the plane.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

8.

Find the focus of the given parabola.

a)

$F\ \left(-1,5\right)$

b)

$F\left(-1,1\right)$

c)

$F\ \left(-1,3\right)$

d)

$F\ \left(-1,-1\right)$

9.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

10.

By inspection, identify the type of conic section in this general form.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

11.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

12.

What are vertices of the given ellipse?

a)

$V_1\left(-7,1\right),\ V_2\left(1,1\right)$

b)

$V_1\left(-1,1\right),\ V_2\left(-7,1\right)$

c)

$V_1\left(1,1\right),\ V_2\left(-7,1\right)$

d)

$V_1\left(1,1\right),\ V_2\left(7,1\right)$

13.

What is the standard equation given the radius and center of the circle?

a)

b)

c)

d)

14.

A conic section defines a set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

15.

Which among the following is the center of the ellipse described in the equation?

a)

$C\left(3,0\right)$

b)

$C\left(-3,0\right)$

c)

$C\left(0,3\right)$

d)

$C\left(0,-3\right)$

16.

Find the correct asymptote for the given hyperbola.

a)

$y=\pm\frac{3}{5}x$

b)

$y=\pm\frac{5}{3}x$

c)

$y=\pm\frac{3}{5}\left(x-3\right)$

d)

$y=\pm\frac{5}{3}\left(x-3\right)$

17.

A satellite dish is to be constructed in the shape of a paraboloid of revolution. If the receiver placed at the focus is located 2ft above the vertex of the dish, how deep will the dish be?

a)

3 units

b)

3.5 units

c)

4 units

d)

4.5 units

18.

Identify the proper vertices described in the given hyperbola.

a)

$V_1\left(3,0\right),\ V_2\left(-3,0\right)$

b)

$V_1\left(-3,0\right),\ V_2\left(3,0\right)$

c)

$V_1\left(0,3\right),\ V_2\left(0,-3\right)$

d)

$V_1\left(0,-3\right),\ V_2\left(0,3\right)$

19.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

20.

Find the correct center and radius described by the equation.

a)

$r\ =\ \sqrt{18},\ C\ \left(-4,6\right)$

b)

$r\ =\ \sqrt{18},\ C\ \left(4,\ -6\right)$

c)

$r=18,\ C\left(-4,6\right)$

d)

$r=18,\ C\ \left(4,\ -6\right)$

21.

Write an equation for an ellipse with the given characteristics: vertices at (7, -4) (-3, -4); foci at (6, -4) (-2, -4)

a)

$\frac{\left(x-2\right)^2}{25}+\frac{\left(y+4\right)^2}{9}=1$

b)

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

c)

$\frac{\left(x-2\right)^2}{25}-\frac{\left(y+4\right)^2}{9}=1$

d)

$\frac{\left(x+2\right)^2}{9}+\frac{\left(y+4\right)^2}{25}=1$

22.

Write an equation for an ellipse with the given characteristics: length of major axis = 12; foci at (-2, 1) (-2, -9)

a)

$\frac{\left(x-3\right)^2}{25}+\frac{\left(y+6\right)^2}{9}=1$

b)

$\frac{\left(x+4\right)^2}{11}+\frac{\left(y+2\right)^2}{64}=1$

c)

$\frac{\left(x+2\right)^2}{11}+\frac{\left(y+4\right)^2}{36}=1$

d)

$\frac{\left(x-2\right)^2}{25}-\frac{\left(y+4\right)^2}{36}=1$

23.

What value must 'c' be so that the graph of $4x^2+cy^2+2x-2y-18=0$ is a circle?

a)

-8

b)

4

c)

-4

d)

8

24.

Write the pair of parametric equations in rectangular form. (You should also be able to graph the equation) $x=t-5\ \ \ and\ \ y=3t-4$

a)

$y=3x+11$

b)

$y=\frac{11}{3}x+1$

c)

$y=-3x+11$

d)

$y=1.5x-4$

25.

Write an equation for the hyperbola with the given characteristics: vertices (3, 0) (-3, 0); asymptotes $y=\pm\frac{2}{3}x$

a)

$\frac{x^2}{3}-\frac{y^2}{5}=1$

b)

$\frac{x^2}{64}-\frac{y^2}{25}=1$

c)

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

d)

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

26.

Write an equation for the hyperbola with the given characteristics: foci (8, 0) (8, 8); vertices (8, 2) (8, 6)

a)

$\frac{\left(y-4\right)^2}{2}-\frac{\left(x-5\right)^2}{7}=1$

b)

$\frac{\left(y-4\right)^2}{4}-\frac{\left(x-8\right)^2}{12}=1$

c)

$\frac{\left(y-5\right)^2}{4}-\frac{\left(x-2\right)^2}{12}=1$

d)

$\frac{\left(y-4\right)^2}{4}-\frac{\left(x-8\right)^2}{12}=1$

27.

Write a general form equation in the xy-plane for the rotated conic at the given angle: $7\left(x'-3\right)=\left(y'\right)^2,\ \ \ \theta=60\degree$

a)

$x^2-x-\sqrt[]{3}xy+y^2-4\sqrt[]{3}y+4=0$

b)

$3x^2-16x-2\sqrt[]{5}xy+y^2-12\sqrt[]{5}y+84=0$

c)

$4x^2-12x-2\sqrt[]{3}xy+y^2-15\sqrt[]{3}y+64=0$

d)

$3x^2-14x-2\sqrt[]{3}xy+y^2-14\sqrt[]{3}y+84=0$

28.

Write a general form equation in the xy-plane for the rotated conic at the given angle: $\frac{\left(x'\right)^2}{2}+\frac{\left(y'\right)^2}{10}=1,\ \ \ \theta=\frac{\pi}{6}$

a)

$4x^2+2\sqrt[]{3}xy+2y^2-10=0$

b)

$3x^2-14x-y^2-12\sqrt[]{3}y=0$

c)

$5x^2+2\sqrt[]{3}xy+7y^2-16=0$

d)

$4x^2+4\sqrt[]{3}xy+4y^2-4=0$

29.

Which ellipse has the greatest eccentricity?

a)

b)

c)

d)

30.

Write an equation for a parabola with the given focus F and vertex V:

F(2, 8) V(2, 10)

a)

$\left(x-4\right)^2=-8\left(y+10\right)$

b)

$\left(x-2\right)^2=-8\left(y-10\right)$

c)

$\left(x-2\right)^2=-6\left(y-5\right)$

d)

$\left(x-3\right)^2=-5\left(y+10\right)$

31.

Write an equation for a parabola with the given focus F and vertex V:

F(2, 5) V(-1, 5)

a)

$\left(y-5\right)^2=-12\left(x+1\right)$

b)

$\left(y-5\right)^2=12\left(x+1\right)$

c)

$\left(x-5\right)^2=8\left(y+1\right)$

d)

$\left(y+5\right)^2=-12\left(x-1\right)$

32.

Graph the ellipse: $\frac{\left(x-5\right)^2}{49}+\frac{\left(y+3\right)^2}{9}=1$

a)

b)

c)

d)

33.

Use a graphing calculator to graph the conic: $x^2-6xy+y^2-4y-8x=0$

a)

b)

c)

34.

What is the directrix of the parabola
(x - 4)²= 8(y + 3)?

a)

y = - 3

b)

x= 5

c)

y= - 5

d)

y= 2

35.

What is the focus of the following parabola?
(y + 5)²= -12 (x - 2)

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

36.

True or False?
When the x-part is squared, the parabola opens up or down.

a)

True

b)

False

37.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

38.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -2, -4), (-2, 8)
Length of minor axis is 10
What is the center of the ellipse?

a)

( - 2, 2)

b)

(- 2, 4)

c)

(2, -2)

d)

(-2, 1)

39.

What direction does the parabola open?
(y-9)²= -40(x+4)

a)

Up

b)

Down

c)

Left

d)

Right

40.

What is "a" in the equation:
(y-9)²=-40(x+4)

a)

- 10

b)

10

c)

- 40

d)

40

41.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what is the center of this ellipse?

a)

(4, 6)

b)

( - 4, 3)

c)

(6, 4)

d)

(4, -3)

42.

How WIDE will this parabola be?

a)

12

b)

3

c)

(2,3)

d)

24

43.

What number would go in the blank?

a)

-2

b)

-4

c)

-8

d)

-16

44.

Given the following, write the equation of the ellipse.

a)

A

b)

B

c)

C

d)

D

45.

Given this directrix and vertex, what would the equation of the parabola be?

a)

(y-2)² = 12(x-1)

b)

(y-2)² = 6(x-1)

c)

(x-1)² = 12(y-2)

d)

(x-1)² = 6(y-2)

46.

Put the ellipse in standard form

a)

A

b)

B

c)

C

d)

D

47.

What should replace the blue square in the equation?

a)

-8y

b)

-2y

c)

+2y

d)

+8y

48.

Given the equation of the ellipse and the C value, write the foci ordered pair

a)

(4 ± 7.42, -2)

b)

(4, - 2 ± 7.42)

c)

(- 4 ± 7.42, 2)

d)

( - 4, 2 ± 7.42)

49.

Given the equation of the parabola, where would the VERTEX be? (put in standard form)

a)

( 3 , 3)

b)

(24, 3)

c)

( - 24, 3)

d)

(-3, 3)

50.

Which direction does this parabola open?

a)

Up

b)

Down

c)

Left

d)

Right

51.

What are the vertices of the ellipse?

a)

(0, 0)

b)

(7, 1) and (-1, 1)

c)

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

d)

(3, 1)

52.

What type of conic section is $3x^2–y^2–11x–6y+4=0$ ?

a)

Ellipse

b)

Hyperbola

c)

Circle

d)

Parabola

53.

Check the box that shows a parabola.

a)

b)

c)

d)

e)

54.

If the plane cuts the cone in the similar fashion but at a certain angle, then the conic section is an (a) .

55.

What type of conic section is $2x^2+2y^2-4x-16y-9=0$ ?

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

56.

What type of conic section is $x^2-x+3y+6=0$ ?

a)

Hyperbola

b)

Ellipse

c)

Circle

d)

Parabola

57.

What type of conic section is shown?

a)

Ellipse

b)

Parabola

c)

Hyperbola

d)

Circle

58.

When the cutting plane intersects the two cones parallel to their vertical axes and perpendicular to their bases, then the conic section is a _______________.

a)

Parabola

b)

Circle

c)

Hyperbola

d)

Ellipse

59.

These are figures that formed by intersecting two inverted cones and a plane.

a)

Cross Sections

b)

Conic Sections

c)

Circles

d)

Parabolas

60.

Conics are special curves and are classified into four types. What are those?

a)

Ellipse

b)

Cone

c)

Parabola

d)

Hyperbola

e)

Circle

61.

Which equation shows an ellipse?

a)

$y^2+x-3y-15=0$

b)

$2x^2-4y^2+18x+120y-159=0$

c)

$4x^2+4y^2-16y+81=0$

d)

$16x^2+11y^2+54x-61y-121=0$

62.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

63.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

64.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

65.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

66.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

67.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

68.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

69.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

70.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

71.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

72.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

73.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

74.

What type of conic section is this?

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

75.

What type of conic section is this?

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

76.

What type of conic section is this?

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

77.

What type of conic section is this?

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

78.

Identify the Five Parts of 3D Conics

4 lines

79.

Write the general algebraic equation for circle

80.

Write the general algebraic equation for parabola

81.

Write the general algebraic equation for ellipse

82.

Write the general algebraic equation for hyperbola

83.

Who is the great mathematician behind the analytic geometry?

a)

Apollonius of Perga

b)

Ptolemy

c)

Rene Descartes

d)

Euclid

84.

Find the standard equation to this graph

a)

b)

c)

d)

85.

Find the graph to this equation

a)

b)

c)

d)

86.

Find the graph to this equation

a)

b)

c)

d)

87.

Find the graph to this equation

a)

b)

c)

d)

88.

Find the standard equation to this graph

a)

b)

c)

d)

89.

Find the standard equation to this graph

a)

b)

c)

d)

90.

Find the standard equation to this graph

a)

b)

c)

d)

91.

Find the standard equation to this graph

a)

b)

c)

d)

92.

Find the standard equation to this graph

a)

b)

c)

d)

93.

Find the standard equation to this graph

a)

b)

c)

d)

94.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

95.

The focus is always inside the parabola.

a)

true

b)

false

96.

A parabola is the set of all points equidistant from the focus and the directrix.

a)

true

b)

false

97.

All parabolas with a vertical directrix open the left or right.

a)

true

b)

false

98.

True or False?
When the x-part is squared, the parabola opens up or down.

a)

True

b)

False

99.

What direction does the parabola point?

a)

Up

b)

Down

c)

Left

d)

Right

100.

(y-4)² = -8(x+1)
What direction does this parabola open?

a)

up

b)

down

c)

left

d)

right

101.

(y-4)² = -8(x+1)
What are the coordinates for the focus?

a)

(1,4)

b)

(-1,6)

c)

(-1,2)

d)

(-3,4)

102.

(x+3)² = 4(y+5)
What is the equation of the directrix?

a)

x = 4

b)

x = 2

c)

y = -4

d)

y = -6

103.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

a)

y² = 24(x+4)

b)

(y+4)² = -12x

c)

x² = 16(y+4)

d)

(x+4)² = -20y

104.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

105.

Identify the center and the length of a and b.

a)

C: (0,4) a= 25, b=4

b)

C: (0,0) a= 4, b=25

c)

C: (0,5) a= 2, b=5

d)

C: (0,0) a= 5, b=2

106.

Given the following, write the equation of the ellipse.

a)

A

b)

B

c)

C

d)

D

107.

What are the foci of the shifted ellipse?

a)

(-5,1) and (-1,1)

b)

(±√3,0)

c)

(0,1) and (-6,1)

d)

(√3 - 3,1) and (-√3 - 3,1)

108.

See Picture

a)

A

b)

B

c)

C

d)

D

109.

See Picture

a)

A

b)

B

c)

C

d)

D

110.

What is the center of the shifted ellipse?

a)

(0,0)

b)

(-3,1)

c)

(1,-3)

d)

(3,-1)

111.

What is the center of the given equation?

a)

(h, k) = (4, 3)

b)

(h, k) = (-4, -3)

c)

(h, k) = (-4, 3)

d)

(h, k) = (4, -3)

112.

What are the vertices of the ellipse?

a)

(0, 0)

b)

(7, 1) and (-1, 1)

c)

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

d)

(3, 1)

113.

What is the equation for the focus points on an ELLIPSE?

a)

c² = a² + b²

b)

c² = a² - b²

c)

1/4d

d)

(x-h)² + (y-k)² = r²

114.

Which is a horizontal ellipse?

a)

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

b)

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

c)

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

d)

$x^2+\frac{y^2}{49}=1$

115.

What are the vertices of

\frac{x^2}{16}+\frac{y^2}{25}=1?

a)

$\left(-4,\ 0\right)\ and\ \left(4,\ 0\right)$

b)

$\left(0,\ -4\right)\ and\ \left(0,\ 4\right)$

c)

$\left(-5,\ 0\right)\ and\ \left(5,\ 0\right)$

d)

$\left(0,\ -5\right)\ and\ \left(0,\ 5\right)$

116.

How long is the major axis of the given ellipse? Format for answer: k where k is a number. Note: There should be no spaces and no units.

\frac{x^2}{64}+\frac{\left(y+2\right)^2}{49}=1

(a)

117.

Check all the boxes that describe the ellipse

\frac{x^2}{4}+\frac{y^2}{81}=1

a)

The center is $\left(0,0\right).$

b)

The major axis is 81.

c)

The minor axis is 4.

d)

The graph is a horizontal ellipse.

118.

What is the equation of the given graph?

a)

$\frac{x^2}{7}+\frac{y^2}{6}=1$

b)

$\frac{x^2}{14}+\frac{y^2}{12}=1$

c)

$\frac{x^2}{49}+\frac{y^2}{36}=1$

d)

$\frac{x^2}{36}+\frac{y^2}{49}=1$

119.

How far is a focus from the center of the given ellipse? Format for answer: k where k is a number. Note: There should be no spaces and no units.

(a)

120.

How long is the minor axis of the given ellipse? Format for answer: k where k is a number. Note: There should be no spaces and no units.

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

(a)

121.

What are the co-vertices of the given ellipse?

a)

$\left(5,\ -4\right)\ and\ \left(5,\ 2\right)$

b)

undefined

c)

$\left(-1,\ -2\right)\ and\ \left(-1,\ 12\right)$

d)

$\left(0,\ 0\right)\ and\ \left(2,\ 5\right)$

122.

What is the equation of a vertical ellipse whose center is (0, 0), length of the major axis is 12 and length of the minor axis is 10?

a)

$\frac{x^2}{36}+\frac{y^2}{25}=1$

b)

$\frac{x^2}{25}+\frac{y^2}{36}=1$

c)

$\frac{x^2}{144}+\frac{y^2}{100}=1$

d)

$\frac{x^2}{100}+\frac{y^2}{144}=1$

123.

An ellipse is a set of points in which the (a) of the distances from the two foci is constant.

124.

What is the center of the given ellipse? Format for answer: (x,y) where x and y are numbers. Note: There should be no spaces.

\frac{\left(x+5\right)^2}{64}+\frac{\left(y-8\right)^2}{4}=1

(a)

125.

In an ellipse, the largest value among a, b, or c is (a) .

126.

What is the equation to get the foci of the ellipse?

a)

$c^2=a^2-b^2$

b)

$c^2=a^2+b^2$

c)

$c=\sqrt{a-b}$

d)

$c=\sqrt{a+b}$

127.

What are the foci of the given ellipse?
$\frac{x^2}{64}+\frac{y^2}{81}=1$

a)

$\left(-\sqrt{17},\ 0\right),\ \left(\sqrt{17},\ 0\right)$

b)

$\left(0,-\sqrt{17}\right),\ \left(0,\sqrt{17}\right)$

c)

$\left(0,\ -17\right),\left(0,17\right)$

d)

$\left(-17,0\right),\left(17,0\right)$

128.

Identify the conic section represented by the equation:

$-3x^2+18y+3y^2+12y=42$

a)

Ellipse

b)

Hyperbola

c)

Circle

d)

Parabola

129.

Identify the conic section represented by the equation:

$12x^2+6+4y^2=4y^2+24x$

a)

Ellipse

b)

Hyperbola

c)

Circle

d)

Parabola

130.

Identify the conic section represented by the equation:

$35x^2+20y=8-15y^2+70$

a)

Ellipse

b)

Hyperbola

c)

Circle

d)

Parabola

131.

The eccentricity value of a hyperbola can be describe as:

a)

e = 0

b)

0 < e < 1

c)

e = 1

d)

e > 1

132.

All of the following could be eccentricity values for an ellipse except:

a)

$e=\frac{5}{7}$

b)

$e=\frac{4}{3}$

c)

$e=\frac{25}{75}$

d)

$e=\frac{1.4}{7}$

133.

Find the standard form for the equation of a hyperbola given by the equation:

$5x^2-20y^2+50x-80y-55=0$

a)

$\frac{\left(x+5\right)^2}{20}-\frac{\left(y-2\right)^2}{16}=1$

b)

$\frac{\left(x+5\right)^2}{20}-\frac{\left(y+2\right)^2}{5}=1$

c)

$\frac{\left(x+5\right)^2}{50}-\frac{\left(y+2\right)^2}{\frac{25}{2}}=1$

d)

$\frac{\left(x+5\right)^2}{32}-\frac{\left(y+2\right)^2}{8}=1$

134.

Find the equations of the asymptotes of the hyperbola given by the equation:

$\frac{\left(y+7\right)^2}{81}-\frac{\left(x-2\right)^2}{144}=1$

a)

$\left(x-2\right)=\pm\frac{1}{3}\left(y+7\right)$

b)

$y+7=\pm\frac{4}{3}\left(x-2\right)$

c)

$y+7=\pm\frac{3}{4}\left(x-2\right)$

d)

$y+7=\pm\frac{1}{8}\left(x-2\right)$

135.

identify the center of the hyperbola:

$\frac{\left(y+11\right)^2}{37}-\frac{\left(x-4\right)^2}{196}=1$

a)

$\left(-11,\ 4\right)$

b)

$\left(4,\ -11\right)$

c)

$\left(11,\ -4\right)$

d)

$\left(-4,\ 11\right)$

136.

identify the vertices of the hyperbola:

$\frac{\left(x-5\right)^2}{36}-\frac{\left(y+7\right)^2}{256}=1$

a)

$\left(5,-20\right)\&\left(5,6\right)$

b)

$\left(23,-7\right)\&\ \left(-13,\ -7\right)\cdot$

c)

$\left(5,-13\right)\&\left(5,\ -1\right)$

d)

$\left(-1,-7\right)\&\left(11,-7\right)$

137.

identify the coordinates of the foci of the hyperbola:

$\frac{\left(y+11\right)^2}{29}-\frac{\left(x-4\right)^2}{196}=1$

a)

$\left(4,\ -26\right)\ \&\left(4,4\right)$

b)

$\left(19,\ -11\right)\&\left(-11,-11\right)$

c)

$\left(4,17\right)\&\left(4.-9\right)$

d)

$\left(4,\ 2\right)\&\left(4,-24\right)$

138.

Write the equation of a hyperbola with center (-2, 3) ,

one focus point at (8,3) and whose transverse axis has length 8.

a)

$\frac{\left(x+2\right)^2}{16}-\frac{\left(y-3\right)^2}{84}=1$

b)

$\frac{\left(y-3\right)^2}{16}-\frac{\left(x+2\right)^2}{84}=1$

c)

$\frac{\left(x+2\right)^2}{100}-\frac{\left(y-3\right)^2}{16\ }=1$

d)

$\frac{\left(y-3\right)^2}{100}-\frac{\left(x+2\right)^2}{84}=1$

139.

Find the equations of the asymptotes of the hyperbola with

a focus point (5,1) and vertices (5, 11) and (5,5).

a)

$y-8=\pm\frac{3\ \ \sqrt[]{10}}{20}\left(x-5\right)$

b)

$y-8=\pm\frac{2\ \ \sqrt[]{10}}{3}\left(x-5\right)$

c)

$y-8=\pm\frac{3\ \ \sqrt[]{13}}{26}\left(x-5\right)$

d)

$y-8=\pm\frac{3}{7}\left(x-5\right)$

140.

Which point could NOT be a solution to

the system in the given graph?

a)

$\left(19.9,\ 2.9\right)$

b)

$\left(1.7,\ 7.3\right)$

c)

$\left(4.4,\ -6.6\right)$

d)

$\left(16.9,\ -4.0\right)$

141.

Identify the equation of the hyperbola in the given image:

a)

$\frac{\left(y-4\right)^2}{49}-\frac{\left(x+9\right)^2}{81}=1$

b)

$\frac{\left(x+9\right)^2}{81}-\frac{\left(y-4\right)^2}{49}=1$

c)

$\frac{\left(y-4\right)^2}{81}-\frac{\left(x+9\right)^2}{49}=1$

d)

$\frac{\left(x+9\right)^2}{49}-\frac{\left(y-4\right)^2}{81}=1$

142.

FInd the standard form of the equation of

a hyperbola given by the equation:

$3y^2+15=12x^2+6y$

a)

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

b)

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

c)

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

d)

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

143.

The eccentricity of a hyperbola is/could be _____.

a)

0

b)

0.5

c)

1

d)

5

144.

The eccentricity of an ellipse is/or could be ____.

a)

0

b)

0.5

c)

1

d)

5

145.

The eccentricity of a circle is/could be _____.

a)

0

b)

0.5

c)

1

d)

5

146.

The eccentricity of a parabola is/could be _____.

a)

0

b)

0.5

c)

1

d)

5

147.

The eccentricity of an ellipse is the _________ compared to the __________.

a)

Major axis, Minor axis

b)

Focus Distance, Major axis

c)

Minor axis, Major axis

d)

None of these

148.

Suppose that the orbit of a particular planet around the sun with equation $\frac{x^2}{6561}+\frac{y^2}{6084}=1$ where x and y are measured in millions of miles. Find the eccentricity of this ellipse. (Round to the nearest thousandth.)

a)

0.270

b)

0.927

c)

5.889

d)

1.078

149.

Find an equation for the conic with the given information.
Focus at (2, 0)
e = $\frac{1}{2}$

a)

$\frac{x^2}{4}+\frac{y^2}{3}=1$

b)

$\frac{x^2}{16}+\frac{y^2}{12}=1$

c)

$\frac{x^2}{12}+\frac{y^2}{16}=1$

d)

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

150.

Find an equation for the conic with the given information.

Focus at (8, 0)

e = 1

a)

32y = x²

b)

8x = y²

c)

8y = x²

d)

32x = y²

151.

Find the equation of the graph:

a)

b)

c)

d)

152.

The ellipse has vertices at _____.

a)

(+2, 0)

b)

(+3, 0)

c)

(0, +2)

d)

(0, +3)

153.

Find the length of the ellipse's major axis.

a)

3 units

b)

6 units

c)

9 units

d)

18 units

154.

Find the location of the foci of the ellipse.

a)

(0, +√5)

b)

(+5, 0)

c)

(+√5, 0)

d)

(0, +5)

155.

Which of the following gives the standard form equation of a circle with center (-6, -4) and a radius of 16?

a)

(x + 6)² + (y + 4)² = 16²

b)

(x + 6)² + (y + 4)² = 16

c)

(x - 6)² + (y - 4)² = 16²

d)

(x - 6)² + (y - 4)² = 16

156.

Which of the following statements is false about the ellipse?

a)

The length of the minor axis is 4.

b)

The set of all x-values is [-6, 2].

c)

The y-intercepts are at (0, 2+ √3).

d)

The foci are at (-2 + 2√2, 2).

157.

Find the standard form equation of the ellipse with vertices (2,8), (2,-2), and co-vertices (-1,3), (5,3).

a)

b)

c)

d)

158.

Find the standard form equation of an ellipse with the length of its minor axis = 8, and foci at (-2, + 4√3, 3).

a)

b)

c)

d)

159.

What is the eccentricity of the ellipse?

a)

0.63

b)

0.79

c)

0.86

d)

0.74

160.

Graph the ellipse:

a)

b)

c)

d)

Conic Sections Review

Total questions: 160

Worksheet time: 3hrs 14mins

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