Question

A circle is drawn on a coordinate plane with the center point at (-1, 3) and a radius of 5. 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 (-1,3) must equal the radius 5. By the Pythagorean theorem (distance formula),

sqrt[(x - (-1))^2 + (y - 3)^2] = 5.

Square both sides:

(x + 1)^2 + (y - 3)^2 = 25.

This is the circle in standard form. (Expanded/general form: x^2 + y^2 + 2x - 6y - 15 = 0.)