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Grade 10 circle equations, general form worksheets

HSG-GPE.A.1 Algebra

Printable circle equations, general form worksheets for grade 10, aligned to Common Core standard HSG-GPE.A.1. Complete the square to find the center.

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Sample problems

  1. Find the center and radius of the circle x² + y² + 4x − 6y − 3 = 0 center (-2, 3), radius 4
  2. Find the center and radius of the circle x² + y² − 4x + 4y − 41 = 0 center (2, -2), radius 7
  3. Find the center and radius of the circle x² + y² − 2x − 2y − 47 = 0 center (1, 1), radius 7
  4. Find the center and radius of the circle x² + y² − 2x − 4y − 4 = 0 center (1, 2), radius 3
  5. Find the center and radius of the circle x² + y² − 8x + 4y + 16 = 0 center (4, -2), radius 2
  6. Find the center and radius of the circle x² + y² − 2x − 10y + 22 = 0 center (1, 5), radius 2
  7. Find the center and radius of the circle x² + y² + 6x + 6y + 9 = 0 center (-3, -3), radius 3
  8. Find the center and radius of the circle x² + y² − 4x − 4y − 28 = 0 center (2, 2), radius 6

These eight are one sample at medium difficulty — the generator makes a different set every time.

A worked example

Find the center and radius of the circle x² + y² + 4x − 6y − 3 = 0 center (-2, 3), radius 4

  1. Group x and y terms: (x² + 4x) + (y² − 6y) = 3
  2. Complete each square: half of 4 is 2, squared 4; half of -6 is -3, squared 9. Add both to each side
  3. (x + 2)² + (y − 3)² = 3 + 4 + 9 = 16
  4. r² = 16, so r = 4: center (-2, 3), radius 4

Every problem on the answer key can show its steps like this — turn on “Show steps” before downloading.

About these worksheets

Every problem is built backwards from its solution, so the answers are whole numbers and the answer key cannot be wrong. Every sheet is generated fresh, so you can print a new one on the same skill as often as you need — different numbers, same difficulty.

Pick how many problems you want and whether they should be easy, medium or hard, then download a PDF with a matching answer key. The key can show the worked steps for every problem, which is what a parent needs to see where a wrong answer went wrong.

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