Free Printable fa#10

1.

To form an ellipse, the orientation of the cutting plane as it intersects the double napped cone is...

a)

Horizontal

b)

Parallel to one side of the cone

c)

Slightly tilted

d)

Vertical

2.

The sum of the distances from the foci to any point on the ellipse is equivalent the length of the...

a)

Minor axis

b)

Major axis

c)

Covertex

d)

Vertex

3.

The denotation used to indicate the distance from the center of the ellipse to the focus is...

a)

a

b)

b

c)

c

d)

f

4.

The shorter axis of symmetry of an ellipse is called the...

a)

Major axis

b)

Minor axis

c)

Axis of symmetry

d)

Eccentricity

5.

The endpoints of the major axis of an ellipse are called the...

a)

Vertices

b)

Covertices

c)

Foci

d)

Center

6.

The endpoints of the minor axis of an ellipse are called the...

a)

Vertices

b)

Covertices

c)

Foci

d)

Center

7.

The denotation used to indicate the distance from the center of an ellipse to the covertex is...

a)

a

b)

b

c)

c

d)

f

8.

The equation that shows the relationship between the distances of the center the focus, vertex and covertex is...

a)

c² = a² + b²

b)

a² = b² + c²

c)

b² = a² + c²

9.

The standard equation of a horizontal ellipse whose center is at (h, k) is...

a)

b)

c)

d)

10.

The standard equation of a vertical ellipse whose center is at (h, k) is...

a)

b)

c)

d)

11.

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

a)

Ellipse

b)

Circle

c)

Hyperbola

d)

Parabola

12.

Check the box that shows a parabola.

a)

b)

c)

d)

e)

13.

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

14.

What type of conic section is

2x^2+2y^2-4x-16y-9=0

?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

15.

What type of conic section is

x^2-x+3y+6=0

?

a)

Hyperbola

b)

Circle

c)

Ellipse

d)

Parabola

16.

What type of conic section is shown?

a)

Ellipse

b)

Hyperbola

c)

Parabola

d)

Circle

17.

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)

Hyperbola

c)

Circle

d)

Ellipse

18.

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

a)

Cross Sections

b)

Circles

c)

Conic Sections

d)

Parabolas

19.

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

a)

Ellipse

b)

Parabola

c)

Circle

d)

Cone

e)

Hyperbola

20.

Which equation shows an ellipse?

a)

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

b)

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

c)

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

d)

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

21.

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

22.

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 )

23.

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

a)

True

b)

False

24.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

25.

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)

26.

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

a)

Up

b)

Down

c)

Left

d)

Right

27.

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

a)

- 10

b)

10

c)

- 40

d)

40

28.

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)

29.

How WIDE will this parabola be?

a)

12

b)

3

c)

(2,3)

d)

24

30.

What number would go in the blank?

a)

-2

b)

-4

c)

-8

d)

-16

31.

Given the following, write the equation of the ellipse.

a)

A

b)

B

c)

C

d)

D

32.

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)

33.

Put the ellipse in standard form

a)

A

b)

B

c)

C

d)

D

34.

What should replace the blue square in the equation?

a)

-8y

b)

-2y

c)

+2y

d)

+8y

35.

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)

36.

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)

37.

Which direction does this parabola open?

a)

Up

b)

Down

c)

Left

d)

Right

38.

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)

39.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

40.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

41.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

42.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

43.

What are the vertices of the ellipse?

Write the equation in standard form:

a)

(0, 0)

b)

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

c)

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

d)

(3, 1)

44.

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

45.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

46.

What is the equation of the circle shown in the graph?

a)

(x-3)²+ (y+4)² = 9

b)

(x-3)²+ (y+4)² = 3

c)

(x+3)²+ (y-4)² = 9

d)

(x+3)²+ (y-4)² = 3

47.

What is the vertex of the parabola: $x=7\left(y-6\right)^2-2$

a)

(6, -2)

b)

(-6, -2)

c)

(-2, 6)

d)

(-2, -6)

48.

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

49.

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

a)

b)

c)

d)

50.

What is the directrix of the parabola with equation $\left(x-4\right)^2=8\left(y+3\right)$ ?

a)

y = - 3

b)

x= 5

c)

y= - 5

d)

y= 2

51.

What is the focus of the parabola with equation $\left(y+5\right)^2=-12\left(x-2\right)$ ?

a)

(2, - 5)

b)

( -5, 2)

c)

(1 , -5 )

d)

(-1, -5 )

52.

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)

53.

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)

54.

What are the asymptotes of the hyperbola in the picture?

a)

$y=x$ and $y=-x$

b)

$y=2x$ and $y=-2x$

c)

$y=\frac{1}{2}x$ and $y=-\frac{1}{2}x$

d)

$y=2x$ and $y=4x$

55.

Which of the following equations of circle in general form given the center at (3, 4) and radius of 5 units?

a)

(x – 3)² - (y – 4)² = 25

b)

(x – 3)² + (y – 4)² = 25

c)

x² + y²+ 6x - 8y - 25 = 0

d)

x² + y²- 6x - 8y = 0

56.

Which of the following equations of circle in general form given the center at (5, -8) and radius of 11 units?

a)

x² + y² -10x + 16y + 32 = 0

b)

x² + y² -10x + 16y - 32 = 0

c)

(x - 5)² + (y + 8)² = 11

d)

(x - 5)² + (y + 8)² = 121

57.

How can we find the general form of a circle?

a)

divide out the center-radius form

b)

multiply out the center-radius form

c)

factor out the center-radius form

d)

add up the center-radius form

58.

In order to convert from general form to center-radius form, you must ___________.

a)

Multiply out

b)

expand

c)

factor

d)

complete the square

59.

Determine the center and radius: x²+ y²+ 14x - 2y = -1

a)

center= (-7,2) radius= 3

b)

center= (-7,1) radius= 7

c)

center= (-4,1) radius= 5

60.

Determine the equation of the circle in standard form: x²+ y²+ 6x - 12y + 20 = 0

a)

(x-3)² + (y+6)² = 25

b)

(x+3)² + (y-6)² = 25

c)

(x-3)² + (y+6)² = 45

d)

(x+3)² + (y-6)² = 5

61.

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

a)

(x+2)² + (y+3)² = 49

b)

(x+2)² + (y+3)² = 13

c)

(x-2)² + (y-3)² = 49

d)

(x-2)² + (y-3)² = 13

62.

Determine the equation of a circle with center (5,-3) and radius of 9

a)

x²+y²-10x+6y-47=4

b)

x²+y²-10x-6y-47=0

c)

2x²+y²+10x+6y-47=0

d)

x²+y²-10x+6y-47=0

63.

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

a)

(x+2)² + (y+3)² = 49

b)

(x+2)² + (y+3)² = 13

c)

(x-2)² + (y-3)² = 49

d)

(x-2)² + (y-3)² = 13

64.

Determine the equation of a circle with center (5,-3) and radius of 9

a)

x²+y²-10x+6y-47=4

b)

x²+y²-10x-6y-47=0

c)

2x²+y²+10x+6y-47=0

d)

x²+y²-10x+6y-47=0

65.

Determine the equation of the circle in standard form: x²+ y²+ 6x - 12y + 20 = 0

a)

(x-3)² + (y+6)² = 25

b)

(x+3)² + (y-6)² = 25

c)

(x-3)² + (y+6)² = 45

d)

(x+3)² + (y-6)² = 5

66.

Determine the center and radius:
x²+ y²- 10x + 8y -8 = 0

a)

C = (5,-4) r = 7

b)

C = (-5,4) r = 7

c)

C = (-4,5) r = 49

d)

C = (5,-4) r = 49

67.

Determine the center and radius: x²+ y²+ 14x - 2y = -1

a)

center= (-7,2) radius= 3

b)

center= (-7,1) radius= 7

c)

center= (-4,1) radius= 5

68.

What is the radius of the given circle:
x²+y²-10x+8y-23=0?

a)

4

b)

2

c)

8

69.

Write the equation of the circle in general form.

a)

A

b)

B

c)

C

d)

D

70.

Convert the equation of the circle from standard to general.

a)

A

b)

B

c)

C

d)

D

71.

Write the equation of the circle in general form.

a)

A

b)

B

c)

C

d)

D

72.

Convert the equation of the circle from general to standard form.

a)

A

b)

B

c)

C

d)

D

73.

Convert the equation of the circle from standard to general.

a)

A

b)

B

c)

C

d)

D

74.

Identify the center and the radius of the circle in general form.

a)

A

b)

B

c)

C

d)

D

75.

What is the orientation of the hyperbola?

\frac{x^2}{4}-\frac{y^2}{25}=1

a)

vertical

b)

horizontal

76.

What is the center of this hyperbola?

a)

(-2,4)

b)

(4,2)

c)

(3,3)

d)

(5,3)

77.

Identify the vertices of the hyperbola:

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

a)

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

b)

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

c)

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

d)

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

78.

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)

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

79.

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)

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

80.

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)

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

fa#10

Total questions: 80

Worksheet time: 3hrs 1mins

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