Talk:HSC Extension 1 and 2 Mathematics/3-Unit/Preliminary/Parametrics

Needs:
 * equations of chords of contact of the tangents from an external point
 * analytical proof of the following geometrical properties: (perhaps with some pretty diagrams?)
 * the tangent to a parabola at a given point is equally inclined to the axis and the focal chord through the point. The significance of this result in the principle of the parabolic reflector should be mentioned.
 * the tangents at the extremities of a focal chord intersect at right angles on the directrix
 * simple locus problems, i.e: "The normals to the parabola $$x^2 = 4ay$$ at the points $$P_1$$ and $$P_2$$ intersect at $$Q$$. If the chord $$P_1P_2$$ varies in such a way that it always passes through the point $$(0, -2a)$$, show that $$Q$$ lies on the parabola."

Nornagon 08:08, 13 March 2007 (UTC)