Answer:
The distance formula is a formalization of the Pythagorean Theorem using x and y coordinates. In other words, they are the same thing in two seemingly different contexts. Every point (x,y) on the circle is related to the circle's center (a,b) by the fact that the distance between the point and the center is a constant (the radius of the circle, r). Equation of a circle is exactly the Pythagorean theorem with specific values plugged in.
Explanation: