L is a straight line in x-y plane. its equation is in the form y-8=m(x-1)

Question

determine all points in x-y plane where line L intersects curve y=2x^2

i know that 1,8 is a point on the line.

I'm not sure what points the question is looking for here. Without knowing what m is, every point except (1,2) is intercepted for some real m. You're correct, (1,8) is a point on the line, but that's not enough information to determine what points are intersected on the parabola.