What is the standard form of the equationcenter (-14,5), circumference: 22π

The standard equation for a circle with center at (h,k) and radius r is

(x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle.

The formula for the circumference of a circle is C = 2pi*r.  In this particular problem, we need to determine the radius of the circle.  That radius is:  r = C/[2pi].  Here, C = 22pi, so we get r = 22pi/[2pi], and so r^2 = 11^2.

Putting to use the given info, we have:

(x+14)^2 + (y-5)^2 = 11^2