or, simplifying,
which is the equation of an ellipse when b2 has a positive sign, and of a hyperbola when b2 has a negative sign. We have thus identified point-rows of the second order with the curves given by equations of the second degree.
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.)