A circle is the set of all points in a plane that are the same distance from the center. Suppose we have a circle centered at (0, 0). If (x, y) is a point on the circle, then the distance from the center to this point would be the radius, r. Given any point on the circle, x is the horizontal distance to y-axis and y is the vertical distance to x-axis. This forms a right triangle. From the Pythagorean Theorem, the equation of a circle centered at the origin is x2+y2=r2.
Now, suppose the center of the circle is moved to point (h, k). From the Distance Formula, where the distance d between any 2 points (x1, y1) and (x2, y2) can be expressed as
d2 = (x2-x1)2 + (y2-y1)2
We can derive the equation of a circle at center (h, k) to be:
r2 = (x - h) 2 + (y- k) 2
