For what value of c will the circle with equation x^2 - 10x + y^2 + 8y + c = 0 have a radius of length \(1\)?
+37157 (x^2 -10x) + ( y^2 + 8y) = - c complete the square for x and y
(x-5)^2 + ( y +4)^2 = - c + 25 + 16 < === the red portion = radius squared
- c + 41 = 1 ^2
-c = - 40 c = 40
