Proof (a) Prove that if any two tangent lines to a parabola intersect at right angles, then their point of intersection must lie on the directrix. (b) Demonstrate the result of pan (a) by showing that the tangent lines to the parabola x 2 − 4 x − 4 y + 8 = 0 at the points ( − 2 , 5 ) and ( 3 , 5 4 ) intersect at right angles and that their point of intersection lies on the directrix.
Proof (a) Prove that if any two tangent lines to a parabola intersect at right angles, then their point of intersection must lie on the directrix. (b) Demonstrate the result of pan (a) by showing that the tangent lines to the parabola x 2 − 4 x − 4 y + 8 = 0 at the points ( − 2 , 5 ) and ( 3 , 5 4 ) intersect at right angles and that their point of intersection lies on the directrix.
Solution Summary: The author explains that if two tangent lines intersect at right angles, the point of intersection must lie on the directrix of parabola.
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Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY