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Equation of a Circle Geometry - Printable Mathematics Worksheets - Wayground

Equation of a Circle Geometry

14 questions

10th - 10th Grade

Mathematics

Equation of a Circle Geometry is a free printable Grade 10 mathematics worksheet that develops students’ ability to write, interpret, and apply the standard equation of a circle, (x − h)² + (y − k)² = r². Across 14 multiple-choice questions, students identify centers and radii, construct equations from center-and-radius information, use diameter to find radius, and recognize equations represented by graphs. The worksheet also includes algebraic reasoning with circles. Students convert general-form equations to standard form by completing the square, determine whether a point lies inside, outside, or on a circle, and identify circle features from equations. It is suitable for guided practice, independent review, or a formative check after instruction. A complete answer key is included to support efficient grading and discussion of common errors.

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Worksheets

Equation of a Circle Geometry

Total questions: 14

Name
Class
Date
1.
Write the equation of a circle with center (7, 0) with radius 3.
a)
(x - 7)2 + y2 = 9
b)
x2 + (y -7)2 = 9
c)
(x - 7)2 + y2 = 3
d)
x2 + (y -7)2 = 3
2.
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
3.
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
4.
What is the equation for this circle?
a)
(x+1)+(y+1)=9
b)
x²+y²=9
c)
x+y=9
5.
What is the equation of a circle with radius 2 and center (3, 4)?
a)
(x+3)2 + (y+4)2 = 2
b)
(x-3)2 + (y-4)2 = 2
c)
(x+3)2 + (y+4)2 = 4
d)
(x-3)2 + (y-4)2 = 4
6.
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
7.
A circle has the equation  x2 + y2 - 12x + 8y + 3 = 0.  Use completing the square to 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
8.
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
9.
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
10.
What is the center of the circle with equation x2 + y2 = 1?
a)
(1, 1)
b)
(0, 0)
c)
not enough information
11.

Prove or disprove that the point (5,4) is on the circle centered at (-1,-2) with a radius of 5.

a)

Yes, it is on the circle

b)

No, it is inside the circle

c)

No, it is outside the circle

d)

No, it is on the circle

12.

Prove or disprove the point (8,8) is on the circle centered at the point (0,2) with a radius of 10.

a)

Yes, it is on the circle.

b)

No, it is outside the circle

c)

No, it is inside the circle

d)

Yes, it is outside the circle

13.

What is the center and radius given the equation, 8x+x2-2y+y2-64=0?

a)

Center: (-4, 1), Radius: 9

b)

Center: (4,1), Radius: 9

c)

Center: (1,-4), Radius: 81

d)

Center: (-4, 1), Radius: 81

14.
Which graph corresponds to 
(x)2+ (y-6)2=9
a)
A
b)
B
c)
C
d)
D
Answer Key

Equation of a Circle Geometry

Total questions: 14

1.
a) (x - 7)2 + y2 = 9
2.
a) Center (4,3)
Radius = 5 units
3.
c) (x+1)2 + (y +1)2 = 9
4.
b) x²+y²=9
5.
d) (x-3)2 + (y-4)2 = 4
6.
c) (x+1)2 + (y +1)2 = 9
7.
a) (x - 6)2 + (y + 4)2 = 49
8.
b) (x-2)2+(y+6)2=48
9.
c) (x + 5)2 + (y - 2)2 = 36
10.
b) (0, 0)
11.
c)

No, it is outside the circle

12.
a)

Yes, it is on the circle.

13.
a)

Center: (-4, 1), Radius: 9

14.
b) B

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FAQs

What does this Equation of a Circle Geometry worksheet cover?

This Grade 10 worksheet uses 14 multiple-choice questions to practice writing and interpreting circle equations in standard form, (x − h)² + (y − k)² = r². Students identify centers and radii, build equations from given information, convert general form by completing the square, classify points as inside, outside, or on a circle, and match an equation to its graph.

How can I use this worksheet to teach writing and interpreting circle equations?

Introduce the standard form by having students identify h, k, and r from an equation, then model how center signs change when coordinates appear in parentheses. Use the construction questions to move from a center and radius to an equation, and follow with the completing-the-square items to connect standard and general forms. Discuss how students can compare a point’s distance from the center with the radius before completing the point-location questions.

What mistakes should I watch for on this circle equations worksheet?

Watch for students reversing the signs of the center coordinates, using the radius instead of r² on the right side, or treating a diameter as the radius. In the completing-the-square questions, students may lose the constant balance or misread the resulting center signs. For point-location items, check that students compare the distance to the radius rather than deciding from one coordinate alone.

How do I assign and grade this Equation of a Circle Geometry worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key for the 14 multiple-choice questions, covering circle equations, completing the square, point location, and graph interpretation. For printable submissions, scan student work with the Wayground for Teachers app to grade it efficiently.

How can I differentiate this circle equations worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation choices and algebraic expressions are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language. These options can make the standard-form equations, completing-the-square items, and multiple-choice choices more accessible without changing the mathematical content.

Where can I find more 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 support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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