How can the equation of a circle be derived?

Answer 1

Suppose the circle has centre (a, b) and radius r.Then, by definition, every point, (x, y) on the circle is at a distance r from (a, b).

That is, sqrt[(x - a)^2 + (y - b)^2] = r

Squaring both sides gives (x - a)^2 + (y - b)^2 = r^2.