Question

A circle is drawn on a coordinate plane with the center point at (-2, 0) and a radius of 7. 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 horizontal distance to the center (-2,0) is x - (-2) = x + 2 and the vertical distance is y - 0 = y. By the Pythagorean Theorem, the distance squared equals the radius squared:

(x + 2)^2 + y^2 = 7^2 = 49.

This is the standard form. Expanded form: x^2 + y^2 + 4x - 45 = 0.