Equation of Circle Worksheets

Printable “Coordinate Geometry” worksheets:
Ordered Pairs (Four Quadrants)
Symmetry in the Coordinate Plane
Coordinate Plane (Horizontal & Vertical Distance)
Equation of Circle

Examples, solutions, videos, and worksheets to help Geometry students learn how to write the equation for a circle in center-radius form, (x-a)² +(y-b)² = r², using the Pythagorean theorem or the distance formula. Write the equation of a circle given the center and radius. Identify the center and radius of a circle given the equation. Complete the square in order to write the equation of a circle in center-radius form. Recognize when a quadratic in x and y is the equation for a circle.

Equation of Circle

The equation of a circle in the coordinate plane describes all the points that are equidistant from a central point, called the center. Recognizing and interpreting the equations of circles involves understanding the standard form and the general form of the circle’s equation.

Standard Form of a Circle:
The standard form of the equation of a circle is:
(x - h)² + (y - k)² = r²
where:
(h, k) is the center of the circle
r is the radius of the circle

Key Points to Remember:
The equation of a circle is always in the form of squared terms for both x and y.
The coefficients of the squared terms must be equal.
The signs within the parentheses indicate the coordinates of the center.
The constant term on the right side of the equation is the square of the radius.

General Form of a Circle:
Sometimes, the equation of a circle is given in a general form:
x² + y² + Dx + Ey + F = 0
To identify the center and radius from this form, you typically need to complete the square for both x and y terms and rewrite the equation in standard form.

Have a look at this video if you need to review how to write the general equation of a circle in standard form.

• Write General Equation of a Circle in Standard Form

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More Equation of Circle Worksheets

Printable
(Answers on the second page.)
Standard Form
Equation of Circle Worksheet #1
Equation of Circle Worksheet #2
Equation of Circle Worksheet #3
Equation of Circle Worksheet #4
Equation of Circle Worksheet #5
Equation of Circle Worksheet #6
General Form & Standard Form
Equation of Circle Worksheet #7
Equation of Circle Worksheet #8
Equation of Circle Worksheet #9
Equation of Circle Worksheet #10

Related Lessons & Worksheets

Equation of Circle

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