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. ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = d Substitute ( x 1 , y 1 ) = ( h , k ) , ( x 2 , y 2 ) = ( x , y ) and d = r . ( x − h ) 2 + ( y − k ) 2 = r Square each side. ( x − h ) 2 + ( y − k ) 2 = r 2 The equation of a circle with center ( h , k ) and radius r units is ( x − h ) 2 + ( y − k ) 2 = r 2 . |