Question

I know the center's (-1, 3), I just can't figure out how to get the correct radius.

Answer 1

If you know the center is at (-1,3), then find r by writing out the standard formula for the equation of a circle, as follows:

(x-2)^2 + (y-5)^2 = r^2

We still have the other point to deal with:  (-4,1).  Subst. -4 for x in this equation, and 1 for y:

(-4-2)^2 + (1-5)^2 = r^2.  Then 36 + 16 = r^2,

and 52 = r^2, so that the radius is positive sqrt(52).

You could write that as sqrt(4)sqrt(13) = 2sqrt(13).  Take your pick.