Free Printable Circles and Ellipses

1.

Write the equation of the circle with a Center at (5,3) that is tangent to the x-axis.

a)

$\left(x-3\right)^2+\left(y-5\right)^2=25$

b)

$\left(x-5\right)^2+\left(y-3\right)^2=25$

c)

$x^2+y^2=9$

d)

$\left(x-5\right)^2+\left(y-3\right)^2=9$

2.

Find the equation of a circle with endpoints of a diameter (−3,1) and (9,-3).

a)

$\left(x-3\right)^2+\left(y+1\right)^2=\sqrt{40}$

b)

$\left(x+3\right)^2+\left(y-1\right)^2=40$

c)

$\left(x-3\right)^2+\left(y+1\right)^2=40$

d)

$x^2+y^2=\sqrt{29}$

3.

Write the equation of the circle with a Center at (-2,5) that is tangent to the y-axis.

a)

$\left(x+2\right)^2+\left(y-5\right)^2=4$

b)

$\left(x+5\right)^2+\left(y-5\right)^2=25$

c)

$x^2+y^2=4$

d)

$\left(x-2\right)^2+\left(y+5\right)^2=25$

4.

In the equation (x-4)²+(x-3)²=25, the center of the circle is at...

a)

(-3, -4)

b)

(4, 3)

c)

(-4, -3)

d)

(3, 4)

5.

The endpoints of a diameter of a circle are (3,1) and (9,5).Find the equation of the circle?

a)

$\left(x-6\right)^2+\left(y-3\right)^2=13$

b)

$\left(x-3\right)^2+\left(y-6\right)^2=132$

c)

$\left(x-6\right)^2+\left(y-3\right)^2=\sqrt{13}$

d)

$\left(x-9\right)^2+\left(y-5\right)^2=132$

6.

Graph the ellipse: $\frac{\left(x-4\right)^2}{16}+\frac{y^2}{49}=1$

a)

b)

c)

d)

7.

In the equation (x+2)²+(y+3)²=49, the radius of the circle is...

a)

14

b)

98

c)

7

d)

49

8.

What are the major vertices of the ellipse in this picture?

a)

(2, 0), (–2, 0)

b)

(0, 2), (0, –2)

c)

(0, 4), (0, –4)

d)

(4, 0), (–4, 0)

9.

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

10.

What is the equation of the circle, with center (-4,5) and radius 6 units?

a)

(x - 4)² + (y + 5)² = 6

b)

(x - 4)² + (y + 5)² = 36

c)

(x + 4)² + (y - 5)² = 6

d)

(x + 4)² + (y - 5)² = 36

11.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

12.

Write the equation of the circle with center (2,-3) and containing (6,−5)?

a)

(x-2)²+(y+3)²=20

b)

(x+3)²+(y−8)²=-20

c)

(x-6)²+(y+5 )²=20

d)

(x-2)²+(y+3)²=164.

13.

Which equation defines the ellipse shown?

a)

b)

c)

d)

14.

What are the major vertices of the ellipse?

a)

(0, 0)

b)

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

c)

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

d)

(3, 1)

15.

What are the minor vertices of the ellipse?

a)

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

b)

(0, 0) and (2, 0)

c)

(4, 0) and (6, 0)

d)

(1, 6) and (1, 4)

16.

Change the following equation to standard form
x²+y²-4x+12y-8=0

a)

(x+2)²+(y-6)²=48

b)

(x-2)²+(y+6)²=48

c)

(x-6)²+(y-2)²=48

d)

(x+2)²+(y-6)²=48

17.

Find the major vertices.

a)

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

b)

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

c)

(3 , 6) and (3 , 4)

d)

(√12 , 4) and (4 , √12)

18.

What are the major vertices of the ellipse in this picture?

a)

(2, 0), (–2, 0)

b)

(0, 2), (0, –2)

c)

(0, 4), (0, –4)

d)

(4, 0), (–4, 0)

19.

Match the graph of the ellipse.

a)

A

b)

B

c)

C

d)

D

20.

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

a)

4

b)

2

c)

8

21.

What are the major vertices of this Ellipse?

a)

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

b)

(-2, 8), (-2, 2)

c)

(-2, 12), (-2, -2)

d)

(-9, 5) , (5, 5)

22.

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

Circles and Ellipses

Total questions: 22

Worksheet time: 3hrs 36mins

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