For what value of c will the circle with equation x^2 + 6x + y^2 - 14y + c = 0 have a radius of length 4?
Put it into standard form by completing the square for x and y
(x+3)^2 + (y -7)^2 = - c + 9 + 49 Right side needs to equal 4^2 (radius squared)
58 - c = 16
c = 42