Equation of a Circle
A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)
A line segment connecting two points on the circle and going through the center is called a diameter of the circle.
Assume that ( x , y ) are the coordinates of a point on the circle shown. The center is at (h, k), and the radius is r .
Use the Distance Formula to find the equation of the circle.
Substitute ( x1, y1 ) = (h, k), (x2, y2) = (x, y), and d = r .
Square each side.
The equation of a circle with center (h, k) and radius r units is .
