Standard form, (x − h)² + (y − k)² = r², is written to be read: the center and the radius are both sitting in it. These free printable worksheets give eight circles in standard form and ask for the center and radius of each — which is exactly where two easy slips live.
If they get stuck
The answer key prints on a separate page.
Two things are turned round on the way out, and a page of these is about nothing else. (x − 3)² puts the center at x = 3, not −3, because the bracket is zero when x is 3; (y + 6)² puts it at y = −6. And the right-hand side is r², so (x − 1)² + (y + 6)² = 4 has a radius of 2, not 4. A student who copies the numbers straight off gets every question wrong in one of those two ways, and there is no arithmetic along the way to catch it.
Half of every sheet is circles whose center sits on an axis: x² + (y + 2)² = 36, (x − 4)² + y² = 100. A bare x² means the center's x-coordinate is 0 — the circle is centered on the y-axis — not that the question has lost a number. A circle centered at the origin never appears, because x² + y² = 25 has no bracket to read.
Find the center and radius of x² + (y + 2)² = 36