Why does 'a' have 2 values if y= x is tangent to parabola y = x^2 + ax + 1. I thought there would be only 1 solution.

Similarly, why are there 2 valus of 'm' when y = mx - 0.5 is tangent to y = x^2 + 5x?

There is only 1 solution for b when y = -x is tangent to y = x^2 + x + b ??