I have this question on circles
For what value of $c$ will the circle with equation $x^2 - 10x + y^2 + 10y + c = 0$ have a radius of length 1?
Rearrange as
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
To have a radius of 1
50 - c = 1
50 - 1 = c
49 = c
+819 
