For what values of a and b is the line 4x + y = b tangent to the parabola y = ax^2 when x = 4?

Answer 1

The equation of the line is y=b-4x with slope = -4

The parabola has slope 2ax and at x=4 this is 8a

Therefore 8a=-4 and a = -1/2.

But the tangent and the line must share the same point, namely (4,-8) (from y=(-1/2)x²)

Therefore -8=b-4*4 and b=8