Well, let's recall just what a circle is. A circle is all the points which are the similar distance, r - called the radius, from a point, ( h, k ) - called the center. In other terms, if ( x, y ) is any point that is on the circle then it has a distance of r from the center, ( h, k ) .
If we empolye the distance formula on these two points we would get,
Or, if we square both sides we get,
( x - h )2 + ( y - k )2 = r 2
This is the standard form of the equation of a circle with radius r and center ( h, k ) .