PROBLEMS
1. Draw a chord of a given conic which shall be bisected by a given point P.
2. Show that all chords of a given conic that are bisected by a given chord are tangent to a parabola.
3. Construct a parabola, given two tangents with their points of contact.
4. Construct a parabola, given three points and the direction of the diameters.
5. A line u' is drawn through the pole U of a line u and at right angles to u. The line u revolves about a point P. Show that the line u' is tangent to a parabola. (The lines u and u' are called normal conjugates.)
6. Given a circle and its center O, to draw a line through a given point P parallel to a given line q. Prove the following construction: Let p be the polar of P, Q the pole of q, and A the intersection of p with OQ. The polar of A is the desired line.