Question

If a circle has a center at the point (3, 4) and goes through the point (6, 8), what is the radius?

Answer 1

Start with the eqn of a circle with center at (h,k) and radius r:

(x-3)^2 + (y-4)^2 = r^2.  Now replace x with 6 and y with 8:

(6-3)^2 + (8-4)^2 = r^2
 
3^2 + 4^2 = r^2  =>  r = 5.