Deriving the Equation of a Circle Using the Pythagorean Theorem

This video tutorial explains how to derive the equation of a circle centered at the origin using the Pythagorean theorem. It begins with a review of the Pythagorean theorem and its application to right triangles. The tutorial then defines a circle and its properties, such as the center and radius. By applying the Pythagorean theorem, the video derives the equation x^2 + y^2 = r^2 for a circle centered at the origin. Examples are provided to illustrate how to find the equation of specific circles and determine if points lie on them.

What is the significance of the center of a circle in relation to its equation?

Explain how to write the equation of a circle given its radius.

How can you determine if a point lies on a circle given its equation?