Hello, StaryNight!

Your preliminary work is correct!Find the coordinates of the point of intersection of the tangents to

at the points at which it meets the line

The slope of the tangent is given by: .

The parabola and line intersect at: .

At , the slope is:

The equation of the tangent is: .

At , the slope is:

The equation of the tangent is: .

Now find where the two tangents intersect . . .