Conic sections
Graphing circles worksheets
Read a circle in standard form, find its center and radius, and graph the complete circle on an equal-scale coordinate grid.
Preview and downloadConic sections practice
Writing equations of circles worksheets
Write exact standard-form circle equations from centers, radii, points, diameters, translations, area, circumference and tangent lines.
Ready-made English PDF · fixed settings
Customization below makes a separate PDF.
Fixed English ready-made files. Custom settings below apply only to the configured PDF.
Ready to print
Start with a ready-made worksheet
Write each circle equation in standard form.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetPaper sizes and printing help · More conic sections activities
Turn geometric facts into standard form
Each worksheet contains ten prompts drawn from centers and radii, three points, translations, diameter endpoints, area, circumference, a point on the circle or a tangent line.
Find the exact center and radius squared first. Then substitute them into (x − h)² + (y − k)² = r².
The separate key gives the exact standard-form equation for every construction.
Learning objective
What this activity builds
Use geometric information to construct an exact circle equation in standard form.
Worked example
Write the equation of the circle with center (2, −3) and radius 5.
(x − 2)² + (y + 3)² = 25.
Substitute h = 2, k = −3 and r² = 25 into (x − h)² + (y − k)² = r².
Teaching notes
Make the practice count
- Identify the center before finding radius squared.
- For diameter endpoints, use the midpoint for the center and one quarter of the endpoint distance squared for r².
- Keep fractional centers and radius squared exact.
- Check translated centers by applying the stated horizontal and vertical changes.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one or more construction forms, then change the seed for a reproducible set of ten circle equations.
Enlarged pages scroll. PDF size stays the same.
A useful next step
Related activities
Conic sections
Properties of circles worksheets
Find exact circle centers and positive radii from standard and rearranged general equations using whole numbers, fractions and radicals.
Preview and download
Pythagorean theorem
Distance between two points worksheets
Find distances on four coordinate grids with whole-number, decimal-tenths, radical or mixed coordinates. Choose first-quadrant or four-quadrant points and print separate worked solutions.
Preview and download