help! fast!

X^2 -10x   + 25   +  y^2 + 6y   +   9   = -c   + 25 + 9

(x-5)^2  +  (y+3)^2  = -c  + 34           

-c+34 = 1

-c=-33

c = 33

Thanks, EP! Amazing!

Completing the square gives us $(x - 5)^2 + (y + 3)^2 = 34 - c$ . Since we want the radius to be 1, we must have $34 - c = 1^2$ . It follows that $c = \boxed{33}$.