- A chord with length is perpendicular to the axis of the parabola . If and are the points where the chord and the parabola meet, prove that the vector from to is perpendicular to the vector from to .
- Show that the length of the chord of a parabola drawn through the focus and parallel to the directrix (the
*latus rectum*) is twice the distance from the focus to the directrix. Next, show that the tangents to the parabola at both ends of this chord intersect the axis of the parabola on the directrix.

**Incomplete.**