MediumConic sections

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.5 Parabolas, Ellipses, and Hyperbolas, #29 · Geometry · Conic sections

The slope of the normal line in Figure A is

This problem is about parabolas, are about ellipses, are about hyperbolas.

The slope of the normal line in Figure A is $s = - 1/ (slope of tangent) =______$ . The slope of the line from $F_{2}$ is $S =______$ . By the reflection property,
$S = cot 2 θ = \frac{1}{2} (cot θ - tan θ) = \frac{1}{2} (s - \frac{1}{s}) .$
Test your numbers $s$ and $S$ against this equation.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.5 Parabolas, Ellipses, and Hyperbolas, #29

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