Geometry · Circles
Equation of a Circle
HSG-GPE.A.1
Definition
(x − h) squared + (y − k) squared = r2, with center (h, k) and radius r.
Examples
- A circle centered at (2, 3) with radius 5 has the equation (x − 2) squared + (y − 3) squared = 25.
- A circle centered at the origin with radius 4 has the equation x2 + y2 = 16.
Key rule
The center's coordinates are subtracted from x and y, and the right side is the radius squared.
Memory hook
(x − h) squared + (y − k) squared = r2 — center (h, k), radius r.