For what value of c will the circle with equation x^2 - 10x + y^2 + 8y + c = 0 have a radius of length 1?
Put in standard circle equation form (x-h)^2 + (y-k)^2 = r^2
(x-5)^2 + (y+4)^2 = - c +25 + 16
so - c + 25 + 16 = 1^2
-c = 1 -25-16
c = 40