Question

A circle is drawn on a coordinate plane with the center point at (-8, -2) and a radius of 2. Derive the equation of the in standard form, using the given information and the Pythagorean Theorem.

Answer 1

Let (x,y) be any point on the circle. The distance from (x,y) to the center (-8,-2) is the radius 2. By the Pythagorean (distance) formula,

sqrt[(x - (-8))^2 + (y - (-2))^2] = 2.

Square both sides:

(x + 8)^2 + (y + 2)^2 = 4.

This is the standard (center-radius) form. Expanded, it becomes

x^2 + y^2 + 16x + 4y + 64 = 0.