Hello, mohamedsafy!

A line can intersect a parabola in 0, 1 or 2 points.1) Prove that the line touches the parabola

and find the coordinates of tangency.

We have: .

Equate [1] and [2]: .

. .

Substitute into [1]: .

The line intersects the parabola at

Since the line intersects the parabola inpoint,one

. . the line is tangent to the parabola.