Worksheets · Precalculus

Precalculus graphing circles worksheet

In Precalculus circles usually start in general form, with everything multiplied out and set to zero. Completing the square on x and on y turns it back into standard form, and then the center and radius can be read off.

Also taught in Algebra 2, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Circles

Date Period

Graph each equation.

  1. Graph (x+5)2+y2=16-10-10-5-500551010
  2. Graph (x−4)2+(y+2)2=25-10-10-5-500551010
  3. Graph x2+y2=25-10-10-5-500551010
  4. Graph (x+1)2+(y+4)2=4-10-10-5-500551010
  5. Graph x2+(y+6)2=4-10-10-5-500551010
  6. Graph (x−2)2+(y−1)2=4-10-10-5-500551010
  7. Graph (x+3)2+(y−2)2=25-10-10-5-500551010
  8. Graph x2+(y−4)2=25-10-10-5-500551010
  9. Graph (x−5)2+y2=9-10-10-5-500551010
  10. Graph (x−2)2+(y+2)2=9-10-10-5-500551010
  11. Graph (x+4)2+(y+4)2=16-10-10-5-500551010
  12. Graph (x+1)2+(y−1)2=25-10-10-5-500551010
  13. Graph (x−4)2+(y−5)2=16-10-10-5-500551010
  14. Graph (x−3)2+y2=25-10-10-5-500551010
  15. Graph (x+3)2+(y−5)2=16-10-10-5-500551010
  16. Graph x2+(y+2)2=9-10-10-5-500551010
  17. Graph (x+2)2+y2=16-10-10-5-500551010
  18. Graph x2+(y−5)2=9-10-10-5-500551010
  19. Graph (x+1)2+(y+4)2=25-10-10-5-500551010
  20. Graph (x−1)2+(y+2)2=9-10-10-5-500551010

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing CirclesAnswer keyVersion 1

Date Period

Graph each equation.

  1. Graph (x+5)2+y2=16-10-10-5-500551010Center (−5,0), radius 4
  2. Graph (x−4)2+(y+2)2=25-10-10-5-500551010Center (4,−2), radius 5
  3. Graph x2+y2=25-10-10-5-500551010Center (0,0), radius 5
  4. Graph (x+1)2+(y+4)2=4-10-10-5-500551010Center (−1,−4), radius 2
  5. Graph x2+(y+6)2=4-10-10-5-500551010Center (0,−6), radius 2
  6. Graph (x−2)2+(y−1)2=4-10-10-5-500551010Center (2,1), radius 2
  7. Graph (x+3)2+(y−2)2=25-10-10-5-500551010Center (−3,2), radius 5
  8. Graph x2+(y−4)2=25-10-10-5-500551010Center (0,4), radius 5
  9. Graph (x−5)2+y2=9-10-10-5-500551010Center (5,0), radius 3
  10. Graph (x−2)2+(y+2)2=9-10-10-5-500551010Center (2,−2), radius 3
  11. Graph (x+4)2+(y+4)2=16-10-10-5-500551010Center (−4,−4), radius 4
  12. Graph (x+1)2+(y−1)2=25-10-10-5-500551010Center (−1,1), radius 5
  13. Graph (x−4)2+(y−5)2=16-10-10-5-500551010Center (4,5), radius 4
  14. Graph (x−3)2+y2=25-10-10-5-500551010Center (3,0), radius 5
  15. Graph (x+3)2+(y−5)2=16-10-10-5-500551010Center (−3,5), radius 4
  16. Graph x2+(y+2)2=9-10-10-5-500551010Center (0,−2), radius 3
  17. Graph (x+2)2+y2=16-10-10-5-500551010Center (−2,0), radius 4
  18. Graph x2+(y−5)2=9-10-10-5-500551010Center (0,5), radius 3
  19. Graph (x+1)2+(y+4)2=25-10-10-5-500551010Center (−1,−4), radius 5
  20. Graph (x−1)2+(y+2)2=9-10-10-5-500551010Center (1,−2), radius 3

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Graph x2+y2−6x+4y−12=0

  1. Group and move the constant: (x² - 6x) + (y² + 4y) = 12.
  2. Add 9 and 4 to both sides: (x - 3)² + (y + 2)² = 25.
  3. Center (3, -2), radius 5.

The answer is Center (3,−2), radius 5.

Where students go wrong

Adding the completing-the-square numbers to one side only. Whatever goes inside the parentheses must also be added to the right side.

Also called plotting circles or center and radius graphs.

What you can put on this worksheet

A circle
Graph (x−1)2+(y−3)2=9 → Center (1,3), radius 3
A radius with a root
Graph, and give the center and radius: x2+(y−1)2=2 → Center (0,1)radius 2

Questions about these worksheets

Yes. Every graphing circles sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the graphing circles questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: a circle and a radius with a root. Tick as many as you want and set how many of each, or let it spread them evenly.

Taking the right side as the radius. It is the radius squared, so 9 means a radius of 3, not 9. The other slip is reading the center with the wrong sign: (x - 2) puts the center at +2.