For what value of c will the circle with equation x^2 + 8x + y^2 + 6y + c = 0 have a radius of length 3?
Complete the square on x , y
(x^2 + 8x + 16) + (y^2 + 6y + 9) = -c + 16 + 9
(x + 4)^2 + ( y + 3)^2 = 25 - c
We need 25 - c = 3^2
So
25 - c = 9
25 - 9 = c
16 = c
