For what value of $c$ will the circle with equation $x^2 - 10x + y^2 + 10y + c = 0$ have a radius of length 1?
x^2 -10x + y^2 + 10y = -c complete the square on x, y
x^2 -10x + 25 + y^2 + 10y + 25 = -c + 25 + 25
-c + 25 + 25 = 1
-c + 50 =1
-c = -49
c = 49
+1222 
