Consider the parabola x = 4y and the focal chord y = 3/4x + 1. (a) Sketch

Consider the parabola x² = 4y and the focal chord y = 3/4x + 1.
 

(a) Sketch the graph of the parabola and the focal chord.

(b) Show that the tangent lines to the parabola at the endpoints of the focal chord intersect at right angles.

(c) Show that the tangent lines to the parabola at the endpoints of the focal chord intersect on the directrix of the parabola.