Free Printable Conics: Ellipses

1.

Which equation defines the ellipse shown?

a)

b)

c)

d)

2.

Center?

a)

(-3 , 2)

b)

(3 , -2)

c)

(12 , 16)

d)

(√12 , 4)

3.

Vertices (endpoints of Major Axis)?

a)

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

b)

(-1 , 2) and (-5 , 2)

c)

(3 , 6) and (3 , 4)

d)

(√12 , 4) and (4 , √12)

4.

Foci?

a)

(-3 , 4) and (-3 , 0)

b)

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

c)

(-3 , -4) and (-3 , 0)

d)

(-3 , 4) and (3 , 0)

5.

Write the standard for for the equation of the ellipse with the given characteristics.

a)

b)

c)

d)

6.

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

7.

What is the center, a and b values for the following equation:
x² + 4y² + 16x - 80y + 320 = 0

a)

(-8, 10); a = 12, b = 6

b)

(-8, 10); a = 6, b = 12

c)

(8, -10); a = 12, b = 6

d)

(8, -10); a = 6, b = 12

8.

Write the equation of an ellipse that has a major axis of 12 units in length, with foci at $\left(\pm5,\ 0\right)$

a)

$\frac{\left(x-5\right)^2}{36}+\frac{\left(y+5\right)^2}{11}=1$

b)

$\frac{x^2}{11}+\frac{y^2}{36}=1$

c)

$\frac{x^2}{36}+\frac{y^2}{11}=1$

d)

$\frac{\left(x+5\right)^2}{11}+\frac{\left(y-5\right)^2}{36}=1$

9.

What is the equation used to find the focal points on an ELLIPSE?

a)

c² = a² + b²

b)

c² = a² - b²

c)

1/4d

d)

(x-h)² + (y-k)² = r²

10.

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)

11.

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

12.

If an ellipse is elongated horizontally then which statement if true?

a)

b² is the denominator of the x² term

b)

a² is the denominator of the x² term

c)

a² is the denominator of the y²term

13.

Find the standard equation of the given ellipse

a)

b)

c)

d)

14.

Find the standard equation of the given ellipse

a)

b)

c)

d)

15.

Find the standard equation of the given ellipse

a)

b)

c)

d)

16.

Find the standard equation of the given ellipse

a)

b)

c)

d)

17.

Find the standard equation of the given ellipse

a)

b)

c)

d)

18.

Find the standard equation of the given ellipse

a)

b)

c)

d)

19.

Find the value of "c" (distance of focus) in the given ellipse

a)

3.60

b)

13

c)

5

d)

2.24

20.

Find the value of "c" (distance of focus) in the given ellipse

a)

invalid

b)

4.12

c)

3.24

d)

3.87

Conics: Ellipses

Total questions: 20

Worksheet time: 38mins

Similar Resources on Wayground