Circles — Equations and Properties

Standard form: (x - h)2 + (y - k)2 = r2

Center = (h, k), radius = r

General form: x2 + y2 + Dx + Ey + F = 0

Complete the square to convert to standard form.

Key properties:

A tangent line touches the circle at one point and is PERPENDICULAR to the radius at that point.

An inscribed angle is half the central angle subtending the same arc.

SAT pattern: "The equation x2 + y2 - 6x + 8y = 0. What is the radius?"

Complete the square: (x-3)2 + (y+4)2 = 25. Radius = 5.

Desmos tip: Type the equation directly. Desmos graphs the circle. Read center and radius visually.

Reference:

Wikipedia: Circle

https://en.wikipedia.org/wiki/Circle