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Find point of intersection of two lines tangent to a parabola

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Let P be the point (3, 9/4). This point lies on the parabola 4y = x^2. A line is drawn through P and the focus of the parabola and intersects another point Q on the parabola. Find the equations of the tangent lines to the parabola at the points P and Q, as well as their point of intersection. Show that those two tangent lines intersect on the directrix of the parabola and are at right angles to each other.

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Solution Summary

A complete, detailed solution of this problem, including general information about parabolas and equations of tangent lines, is provided.

Solution provided by:
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
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