Free Printable Conic Section Overview

1.

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)

2.

What are the co-vertices of the ellipse?

a)

(0, 0)

b)

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

c)

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

d)

(3, 1)

3.

What is the center of the shifted ellipse?

a)

(0,0)

b)

(-3,1)

c)

(1,-3)

d)

(3,-1)

4.

See Picture

a)

A

b)

B

c)

C

d)

D

5.

Find the standard equation of the given ellipse

a)

b)

c)

d)

6.

Find the standard equation of the given ellipse

a)

b)

c)

d)

7.

Find the standard equation of the given ellipse

a)

b)

c)

d)

8.

Which of the following is the graph of $\frac{\left(x+3\right)^2}{4}+\frac{\left(y+1\right)^2}{9}=1$

a)

b)

c)

d)

9.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

10.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

11.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

12.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

13.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

14.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

15.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

16.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

17.

Which is the center of the circle with the equation

(x - 3)² + (y + 5)² = 16

a)

(3, 5)

b)

(-3, 5)

c)

(5, -3)

d)

(3, -5)

18.

Which is the radius of the circle with equation

(x - 2)² + (y + 4)² = 9

a)

81

b)

3

c)

9

d)

4.5

19.

The vertices of a hyperbola are located at (1,1) and (5 ,1). Which are the coordinates of the center?

a)

(3,1)

b)

(3,0)

c)

(1,3)

d)

(9,1)

20.

For the ellipse with the following characteristics:
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)

21.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

22.

Write the equation of the circle with a radius of 3 and a center of (4, 2).

a)

( x - 4)² + (y - 2)² = 3

b)

( x - 2)² + (y - 2)² = 3²

c)

( x - 4)² + (y - 2)² = 3²

d)

( x + 4)² + (y + 2)² = 3²

23.

Why is the graph of the circle incorrect?
(x-3)² + y² = 4

a)

The radius should be 4.

b)

The center should be at (3,0).

c)

The radius should be -2.

d)

The center should be at (-3,0).

24.

Classify the given conic section and match it's characteristics:
(x - 3)² + ( y + 5)² = 25

a)

Ellipse; center (3, -5)

b)

Ellipse; Center (-3, 5) ; radius = 5

c)

Circle; Center (3, - 5) ; radius = 25

d)

Circle; Center (3, - 5) ; radius = 5

25.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

26.

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

27.

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

28.

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

29.

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

30.

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

31.

What conic section is pictured?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

32.

What conic section is pictured?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

33.

Classify the conic section.

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

34.

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 are the a and b values?

a)

a = 6, b = 3

b)

a = 6, b = 4

c)

a = 36, b = 16

d)

a = 4, b = 6

35.

What is the equation for the foci on an ELLIPSE?

a)

c² = a² + b²

b)

c² = a² - b²

c)

1/4d

d)

(x-h)² + (y-k)² = r²

36.

Name the center of the ellipse and the a and b values: $\frac{x^2}{100}+\frac{\left(y+2\right)^2}{25}=1$

a)

Center: (0, -2)

a = 100

b = 25

b)

Center: (0, 2)

a = 10

b = 5

c)

Center: (0, -2)

a=10

b=5

d)

Center: (0, 2)

a=100

b=25

37.

Which correctly describes the parabola: $x=7\left(y-6\right)^2-2$

a)

Opens left

b)

Opens right

c)

Opens up

d)

Opens down

38.

Which correctly describes the parabola: $y=2\left(x-1\right)^2-3$

a)

Opens left

b)

Opens right

c)

Opens up

d)

Opens down

39.

Which correctly describes the parabola: $y=-\frac{1}{2}\left(x+3\right)^2+4$

a)

Opens left

b)

Opens right

c)

Opens up

d)

Opens down

40.

What is the directrix of this parabola?

a)

x = -3

b)

y = -3

c)

x = 3

d)

y = 3

41.

The focus is always inside the parabola.

a)

true

b)

false

42.

Identify the vertex.

a)

A

b)

B

c)

C

d)

D

43.

$y\ =\ a\left(x\ -h\right)^2\ +\ k$ & $x\ =\ a\left(y\ -k\right)^2\ +\ h$ If a is positive, the parabola opens...

a)

up/right

b)

down/left

44.

$y\ =\ a\left(x\ -h\right)^2\ +\ k$ $x\ =\ a\left(y\ -k\right)^2\ +\ h$ If a is negative, the parabola opens...

a)

up/right

b)

down/left

45.

Which parabola equation type is shown?

a)

y =

b)

x =

46.

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

a)

true

b)

false

47.

Identify the conic: 6y² – 5x – 2y + 5 = 0

a)

Parabola

b)

Circle

c)

Hyperbola

d)

Ellipse

48.

What is the equation for the graph?

a)

b)

c)

d)

49.

What is the value of p?
(y - 4)²= -8(x+1)

a)

-8

b)

2

c)

4

d)

-32

50.

Which conic section is represented by the equation $-9x^2+y^2-72x-153=0$ ?

a)

Circle

b)

Ellipse

c)

Hyperbola

d)

Parabola

51.

What is the focus of this parabola?

a)

(1/2,0)

b)

(0,1/2)

c)

(2,0)

d)

(0,2)

52.

What is the directrix of the parabola

$\left(x-4\right)^2=8\left(y+3\right)$

a)

y = - 3

b)

x = 5

c)

y = - 5

d)

y = 2

53.

Which conic's equation has only 1 square?

a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

54.

Which conic's equation has 2 squares with the same signs and different leading coefficents?

a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

55.

Which conic's equation has 2 squares with opposite signs?

a)

Parabola

b)

Circle

c)

Ellipse

d)

Hyperbola

56.

Find the ordered pairs of the vertices of the conic pictured.

a)

(-4, -4) and (6, -4)

b)

(4, 4) and (-6, 4)

c)

(-1, -1) and (-1, 9)

d)

The conic has no vertices.

57.

Find the ordered pair for the focus of the conic pictured.

a)

(5, 4)

b)

(3, 6)

c)

(1, 4)

d)

(3, 2)

58.

Find the equation of the figure shown.

a)

(x-1)²/16 - (y+2)²/4= 1

b)

(x+1)²/16 - (y-2)²/4= 1

c)

(y+2)²/4 - (x-1)²/16= 1

d)

(x-1)²/4 - (y+2)²/2= 1

59.

The foci of an ellipse are located at (-2, 3) & (2, 3), where is the center?

a)

(0, 3)

b)

(3, 0)

c)

(-2, 0)

d)

(2, 0)

60.

The length of the major axis is 6, what is the value of the first denominator in the equation?

a)

6

b)

12

c)

3

d)

9

61.

A hyperbola has vertices at (0, -1) and (4, -1) and foci at (-2, -1) and (6, -1). What is the value of b²?

a)

12

b)

144

c)

4

d)

16

62.

Which of the following is a point of intersection between the line x + y =1 and the ellipse x² + 3y² =21?

a)

(1.5, -3)

b)

(3, -1.5)

c)

(-1.5, 2.5)

d)

(1.5, -1.5)

63.

If a vertex of a horizontal ellipse is at (0, 0) and the length of the major axis is 8, where is the other vertex?

a)

(8, 0)

b)

(0, 8)

c)

(16, 0)

d)

(0, 16)

64.

a)

Vertical Ellipse

b)

Vertical Hyperbola

c)

Horizontal Ellipse

d)

Horizontal Hyperbola

65.

Write an equation for the ellipse with each set of characteristics. Then answer the question.

Vertices ( -7, -3), (13, - 3)

foci ( - 5, -3 ) , (11 , -3)

What is the a and b value of the ellipse? _______________________

a)

(x+7)²/10 + (y+3)²/6 = 1

b)

(x-3)²/100 + (y+3)²/64 = 1

c)

(x+7)²/36 + (y+3)²/100 = 1

d)

(x-3)²/100 + (y+3)²/36 = 1

66.

A hyperbola has vertices (±5, 0) and one focus at (6, 0). What is the equation of the hyperbola in standard form?

What are the equations for the asymptotes?

__________________________________________________

a)

x²/25 + y²/11 = 1

b)

x²/5 - y²/11 = 1

c)

x²/11- y²/25 = 1

d)

x²/25 - y²/11= 1

67.

Check the box that shows a parabola.

a)

b)

c)

d)

e)

68.

What type of conic section is shown?

a)

Ellipse

b)

Hyperbola

c)

Parabola

d)

Circle

69.

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

a)

Cross Sections

b)

Circles

c)

Conic Sections

d)

Parabolas

70.

Conics are special curves and are classified into four types. EXCEPT?

a)

Ellipse

b)

Parabola

c)

Circle

d)

Cone

e)

Hyperbola

71.

What number would go in the blank?

a)

-2

b)

-4

c)

-8

d)

-16

72.

What are the foci of the graph of $\frac{\left(y-1\right)^2}{16}-\frac{\left(x+1\right)^2}{4}=1$

a)

$\left(-1,\ 1\pm2\sqrt{5}\right)$

b)

$\left(1,\ 1\pm2\sqrt{5}\right)$

c)

$\left(1\pm2\sqrt{5},\ 1\right)$

d)

$\left(1,\ 1\pm2\sqrt{5}\right)$

73.

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

a)

(y-2)² = 12(x-1)

b)

(y-2)² = -12(x-1)

c)

(x-1)² = 12(y-2)

d)

(x-1)² = -12(y-2)

74.

What are the foci of the hyperbola with the equation y²/12 - x²/5 = 1

a)

(0, ±√17)

b)

(±√17, 0)

c)

(0, ±√7)

d)

(±√7, 0)

75.

Write the standard form of the Hyperbola that has vertices at (0, 13) and (0, -15) and asymptotes at $y=\frac{7}{5}x-1$ and $y=-\frac{7}{5}x-1$ .

a)

$\frac{\left(y+1\right)^2}{196}-\frac{x^2}{100}=1$

b)

$\frac{y^2}{196}-\frac{\left(x-1\right)^2}{100}=1$

c)

$\frac{x^2}{100}-\frac{\left(y-1\right)^2}{196}=1$

d)

$\frac{x^2}{196}-\frac{\left(y+1\right)^2}{100}=1$

76.

A perfect circle has an eccentricity of ______.

a)

0

b)

.99

c)

1

d)

2

77.

The flattest ellipse before it becomes a line will have an eccentricity of _______.

a)

0

b)

.99

c)

1

d)

2

78.

Which diagram shows a planet with the least eccentric orbit?

a)

1

b)

2

c)

3

d)

4

79.

What is the maximum eccentricity an ellipse can be?

a)

0

b)

.5

c)

1

d)

42

80.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

81.

The 'p' value represents the distance between the vertex and the focus AND the vertex and the directrix.

a)

True

b)

False

82.

The vertex, (h, k), is halfway between the focus and the directrix.

a)

true

b)

false

83.

If the directrix is y = 4 and the focus is at
(3, 0), the value of p is:

a)

8

b)

-8

c)

2

d)

-2

84.

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

a)

true

b)

false

85.

The directrix is parallel to the axis of symmetry.

a)

True

b)

False

86.

Given the graph below, what is the equation of the parabola?

a)

$(x+2)^2=4(y-4)$

b)

$(x+2)^2=(y-4)$

c)

$(x-2)^2=4(y+4)$

d)

$(x-2)^2=(y-4)$

87.

The line containing the center and foci.

a)

Major Axis

b)

Minor Axis

c)

Vertices

d)

Co-Vertices

88.

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 type of an ellipse has the following characteristics?

a)

vertical

b)

horizontal

89.

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

a)

(x - 2)²+ (y + 5)²= 36

b)

(x - 5)² + (y + 2)² = 6

c)

(x + 5)²+ (y - 2)²= 36

d)

(x + 2)²+ (y - 5)²= 6

90.

A circle has the equation x² + y² - 12x + 8y + 3 = 0. Write the equation in standard form.

a)

(x - 6)² + (y + 4)² = 49

b)

(x + 4)² + (y - 6)² = 49

c)

(x - 6)² + (y + 4)² = 55

d)

x² + y² = 55

91.

A circle has the equation x² + y² + 8x - 20 = 0. Write the equation in standard form.

a)

(x + 4)² + y² = 6

b)

(x + 4)² + y² = 36

c)

(x - 4)² + y² = 6

d)

(x - 4)² + y² = 36

92.

What is the equation describing the relationship between dimensions and foci of a hyperbola?

a)

c² = a² + b²

b)

c² = a² - b²

c)

4p

d)

(x-h)² + (y-k)² = r²

93.

What is the value of a² for the given hyperbola?

a)

1

b)

5

c)

25

d)

16

94.

Is the hyperbola vertical or horizontal?

a)

Vertical

b)

Horizontal

95.

What are the vertices of the hyperbola?

a)

(0, 3) and (0, -3)

b)

(-4, 3) and (-4, -3)

c)

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

d)

(4, 0) and (-4, 0)

96.

Determine the value of b

a)

1

b)

2

c)

3

d)

4

97.

What is the "c" value of this hyperbola?

a)

5.83

b)

4.45

c)

3.34

d)

6.5

e)

7.25

98.

The directrix and the axis of symmetry of a parabola are perpendicular.

a)

True

b)

False

99.

Identify the conic represented by the equation without completing the square:
$4x^2-9y^2-8x+12y-144=0$

a)

Parabola

b)

Cirlce

c)

Hyperbola

d)

Ellipse

100.

a)

4

b)

9

c)

6

d)

3

Conic Section Overview

Total questions: 100

Worksheet time: 4hrs 34mins

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