Part of CG-03 — Parabola

Chord of Contact and Related Formulas

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From external point (x1,y1) to y2y^2=4ax: chord of contact is T=0 (yy1=2a(x+x1)), chord with midpoint is T=S1, pair of tangents is T2T^2=S*S1. These are the same T=0 substitution rules used for circles and all conics. The area of the triangle formed by the tangent pair and chord of contact from point P equals S1^3/2(2a)\frac{3/2}{(2a)} (where S1 is the power of the point). The pole of a line with respect to the parabola is found by comparing the polar equation with the given line. The polar of the focus is the directrix, a fundamental result connecting pole-polar theory with the definition.

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