A parabola is the set of all points equidistant from a point (the focus) and a line (the directrix). In this problem, you're asked to pick an arbitrary point on the directrix, find the equations for the two tangent lines to the parabola that go through the arbitrary point on the directrix, and show that the slopes of those two lines are negative inverses of each other. That is, if is a point on the directrix, and line is tangent to the parabola at some point and also contains and has slope and if it's also true that line is tangent to the parabola at some point and also contains point and has slope then you're asked to show that

Does that make sense?