x^2 + y^2 = 9
Differentiate wrt x
2x + 2y*dy/dx = 0
Hence x + y = 0. (because dy/dx = 1), so y = -x
Put this in the original equation to get. 2x^2 = 9
Two solutions: x = 3/sqrt(2) and x = -3/sqrt(2)
Corresponding values of y are y = -3/sqrt(2) and y = 3/sqrt(2) (because y = -x)
Equation of line with slope 1 is y = x + k where k is a constant.
Plug the known pairs of x and y into this equation to find the corresponding values of k.