Skills · Geometry · Circles
The equation of a circle
Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.
Problem types
- the center, from (x − h)² + (y − k)² = r²: (x − 2)² + (y + 3)² = 25
- the radius, from (x − h)² + (y − k)² = r²: (x − 2)² + y² = 20
- the center or radius of a circle on a grid: a circle on the grid
- the center or radius, completing the square first: x² + y² + 6x − 4y − 12 = 0
Sample Sheet · Level 1
- Find the radius of the circle (x + 4)² + y² = 49.
- Find the center of the circle (x + 1)² + (y + 5)² = 81.
- Find the center of the circle (x − 7)² + y² = 81.
- Find the radius of the circle (x − 7)² + (y − 9)² = 16.
- Find the center of the circle (x − 6)² + (y − 9)² = 9.
- Find the radius of the circle (x − 2)² + (y + 9)² = 4.
- Find the radius of the circle (x + 1)² + (y − 3)² = 81.
- Find the center of the circle (x + 3)² + (y − 1)² = 100.
Answer key
- 7 units
- (−1, −5)
- (7, 0)
- 4 units
- (6, 9)
- 2 units
- 9 units
- (−3, 1)
Sample Sheet · Level 3
- Find the radius of the circle x² + y² + 12x − 8y + 3 = 0.
- Find the radius of the circle (x + 1)² + (y + 6)² = 30.
Find the radius of the circle.- Find the radius of the circle (x + 7)² + (y − 4)² = 64.
- Find the radius of the circle x² + y² + 10x + 6y − 61 = 0.
- Find the center of the circle (x + 1)² + (y − 1)² = 9.
- Find the center of the circle (x + 2)² + (y + 4)² = 9.
Find the radius of the circle.
Answer key
- 7 units
- √30 units
- 2 units
- 8 units
- √95 units
- (−1, 1)
- (−2, −4)
- 5 units
Make your own
Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.