Wayground
Equations of Circles - Printable Mathematics Worksheets - Wayground

Equations of Circles

15 questions

9th - 12th Grade

Mathematics

This Grade 9–12 mathematics worksheet gives students focused practice with equations of circles in standard form, (x − h)² + (y − k)² = r². Across 15 multiple-choice questions, students identify the center and radius, write equations from a center and radius, convert diameter to radius, and interpret equations such as x² + y² = 9. The worksheet also asks students to connect equations with visual representations. They select graphs that match given circle equations and determine which equation corresponds to a graph by reading its center and radius. This combination reinforces sign conventions, squared radius values, and the relationship between algebraic and graphical forms. It is designed for Grade 9 through Grade 12 math instruction, review, or assessment. The resource is a free printable worksheet with a complete answer key, making it ready for independent practice, small-group work, or teacher-led review.

Worksheet settings

Font size

S
M
L
XL
Worksheets

Equations of Circles

Total questions: 15

Name
Class
Date
1.

What is the standard equation of a circle?

a)

(x-k)2 + (y-h)2 = r2

b)

(x+h)2 + (y+k)2 = r2

c)

(x-h)2 + (y-k)2 = r2

d)

(k-x)2 + (h-y)2 = r2

2.

What does (h,k) standard for in the standard circle equation?

a)

(h,k) is the center of the circle

b)

(h,k) is a point on the circle.

c)

(h,k) is a point that we guess and find

d)

(h,k) is the radius of the circle

3.

What does the r in the standard equation stand for?

a)

r is the diameter of the circle

b)

r is the radius of the circle

c)

r is the x coordinate of the center of the circle

d)

r is the y coordinate of the center of the circle

4.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)2 + y2 = 9

b)

(x + 7)2 + y2 = 3

c)

(x - 7)2 + y2 = 3

d)

(x + 7)2+ y2 = 9

5.

What is the center and radius of a circle with an equation (x+5)2 + (y-1)2 = 64

a)

Center is (5,-1) and radius is 8

b)

Center is (-5, 1) and radius is 8

c)

Center is (-1, 5) and radius is 8

d)

Center is (-5,1) and radius is 64

6.
What are the coordinates of the center and the radius of the circle with equation:
(x - 4)2 + (y - 3)2 = 25 ?
a)
Center (4,3)
Radius = 5 units
b)
Center (4,3)
Radius = 25 units
c)
Center (-4,-3)
Radius = 25 units
d)
Center (-4,-3)
Radius = 5 units
7.

What is the equation of a circle with radius 4 and center (0, 8)?

a)

x2 + (y-8)2 = 16

b)

x2 + (y-8)2= 4

c)

x2 + (y-8)2 = 4

d)

x2 + (y+8)2 = 16

8.

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

9.

What is the equation for this circle?

a)

(x+1)+(y+1)=9

b)

x²+y²=9

c)

x2+y2=3

10.
Which graph corresponds to 
(x)2+ (y-6)2=9
a)
A
b)
B
c)
C
d)
D
11.

Which graph corresponds to

(x-4)2+ (y+4)2=25

a)

A

b)

B

c)

C

d)

D

12.

Which equation matches the circle on the graph?

a)

(x-2)2+(y+3)2=81

b)

(x+3)2+(y-2)2=9

c)

(x-2)2+(y+3)2=9

d)

(x-2)2+(y-3)2=3

13.

Which equation matches the circle on the graph?

a)

(x+1)2+(y+3)2=4

b)

(x-3)2+(y-1)2=4

c)

(x+3)2+(y+1)2=4

d)

(x+3)2+(y+1)2=2

14.

Which equation matches the circle on the graph?

a)

(x-3)2+(y-4)2=16

b)

(x-5)2+(y-2)2=20

c)

(x+3)2+(y+4)2=16

d)

(x-3)2+(y-4)2=4

15.

Which equation matches the circle on the graph?

a)

(x+2)2+y2=16

b)

(x+2)2+y2=4

c)

(x+4)2+y2=4

d)

(x+20)2+y2=12

Answer Key

Equations of Circles

Total questions: 15

1.
c)

(x-h)2 + (y-k)2 = r2

2.
a)

(h,k) is the center of the circle

3.
b)

r is the radius of the circle

4.
a)

(x - 7)2 + y2 = 9

5.
b)

Center is (-5, 1) and radius is 8

6.
a) Center (4,3)
Radius = 5 units
7.
a)

x2 + (y-8)2 = 16

8.
c)

(x + 5)2 + (y - 2)2 = 36

9.
b)

x²+y²=9

10.
b) B
11.
c)

C

12.
c)

(x-2)2+(y+3)2=9

13.
c)

(x+3)2+(y+1)2=4

14.
a)

(x-3)2+(y-4)2=16

15.
a)

(x+2)2+y2=16

Browse by subjects

Browse by grades

Browse by format

FAQs

What does this equations of circles worksheet cover?

This worksheet builds skill with the standard circle equation, (x − h)² + (y − k)² = r², through 15 multiple-choice questions. Students identify centers and radii, write equations from given coordinates or diameter information, and match equations with graphs, strengthening connections between a circle’s algebraic and visual representations.

How can I use this worksheet to teach equations of circles?

Introduce the roles of h, k, and r in standard form, then model how the signs inside the squared expressions identify the center and how the square root of r² gives the radius. Use the early definition and equation-writing questions to check understanding before having students tackle the graph-matching items. Ask students to explain how a graph’s center and distance from the center determine the equation they select.

What mistakes should I watch for when students complete this circle equations worksheet?

Watch for reversed signs when students read the center from expressions such as (x + 5)² or (y − 1)². Students may also use r² as the radius instead of taking its square root, or use a diameter of 12 as the radius rather than converting it to 6. In the graph questions, check that they identify both the center and the squared radius instead of matching on only one feature.

How do I assign and grade this equations of circles worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 15 multiple-choice items. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital version can be assigned and scored through Wayground.

How can I differentiate this equations of circles worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the equations, answer choices, and graph-matching items are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when that supports access to the mathematical directions and circle notation.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion