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
(x + 5)^2 + ( y -5)^2 = 50 - c
We want
50 - c = 1^2
50 - c = 1
c = 50 - 1 = 49
+2115 
