How to write the equation of a circle when center is at the origin and radius is given

The video tutorial explains how to derive the equation of a circle. It starts with the general equation for a circle with a center at any point (H, K) and then simplifies it for a circle centered at the origin (0, 0). The instructor demonstrates how to substitute the center coordinates and radius into the equation, resulting in the final form: X^2 + Y^2 = 36, where the radius is 6.

Explain how to derive the equation of a circle from its center and radius.

If the radius of a circle is 6, what is the value of r squared in the equation?