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Coordinates That Satisfy the Equation of a Circle in Standard Form - Printable Mathematics Worksheets - Wayground

Coordinates That Satisfy the Equation of a Circle in Standard Form

10 questions

10th - 11th Grade

Mathematics

This Grade 10–11 mathematics worksheet develops students’ ability to interpret and write equations of circles in standard form, (x − h)² + (y − k)² = r². Across 10 multiple-choice questions, students identify a circle’s center and radius, write an equation from a center and radius or diameter, match an equation to its graph, and convert equations between general and standard form by completing the square. The questions reinforce careful attention to signs, squared radius values, and coordinate changes. Students also determine the center and radius from general-form equations, including examples with positive and negative coefficients. This free printable worksheet is suitable for independent practice, review, or a quick formative assessment in Algebra or coordinate geometry, and it includes a complete answer key for efficient checking.

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Coordinates That Satisfy the Equation of a Circle in Standard Form

Total questions: 10

Name
Class
Date
1.
What is the coordinates of the centre and the radius of the circle with equation:
(x - 4)2 + (y - 3)2 = 25 ?
a)
Centre  (4,3)
Radius = 5 units
b)
Centre  (4,3)
Radius = 25 units
c)
Centre  (-4,-3)
Radius = 25 units
d)
Centre  (-4,-3)
Radius = 5 units
2.
What is the equation of the circle, with centre (4,2) and radius 5 units?
a)
(x + 4)2 + (y + 2)2 = 25
b)
(x + 4)2 + (y + 2)2 = 5
c)
(x - 4)2 + (y - 2)2 = 5
d)
(x - 4)2 + (y - 2)2 = 25
3.
What is the coordinates of the centre and the radius of the circle with equation:
(x + 3)2 + (y + 1)2 = 22 ?
a)
Centre  (-3,-1)
Radius = 4 units
b)
Centre  (3,1)
Radius = 2 units
c)
Centre  (-3,-1)
Radius = 2 units
d)
Centre  (3,1)
Radius = 4 units
4.
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
5.
Which graph corresponds to 
(x)2+ (y-6)2=9
a)
A
b)
B
c)
C
d)
D
6.

What is the correct equation of the given circle in general form?

a)

A

b)

B

c)

C

d)

D

7.
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
8.
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
9.
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
10.
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
Answer Key

Coordinates That Satisfy the Equation of a Circle in Standard Form

Total questions: 10

1.
a) Centre  (4,3)
Radius = 5 units
2.
d) (x - 4)2 + (y - 2)2 = 25
3.
c) Centre  (-3,-1)
Radius = 2 units
4.
c) (x + 5)2 + (y - 2)2 = 36
5.
b) B
6.
d)

D

7.
a) (x+2)2 + (y+3)2 = 49
8.
b) (x+3)2 + (y-6)2 = 25
9.
a) C = (5,-4) r = 7
10.
b) (x+3)2 + (y-6)2 = 25

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FAQs

What does this worksheet cover about equations of circles?

This worksheet gives Grade 10–11 students 10 multiple-choice questions on interpreting and writing circle equations in standard form. Students identify centers and radii, use a diameter to find the radius, select a matching graph, and convert general-form equations to standard form by completing the square.

How can I use this worksheet to teach circle equations in standard form?

Introduce the structure (x − h)² + (y − k)² = r², then model how the signs inside the brackets determine the center and how r² determines the radius. Use the early center-and-radius questions before discussing the diameter item, graph selection, and general-to-standard-form questions; ask students to explain why a coefficient such as −10x produces a positive x-coordinate for the center.

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

Watch for students reversing the signs of the center coordinates, treating r² as the radius instead of taking its square root, or using the diameter as the radius. In the conversion questions, students may also lose signs while completing the square, choose the wrong graph, or report the center correctly but calculate the radius incorrectly.

How do I assign and grade this circle-equations worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 10 multiple-choice items. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses through the digital version.

How can I differentiate this worksheet on circle equations?

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the equation choices and graph-based items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support students working with the standard-form and general-form circle questions.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all 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.

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