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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.3 The Slope and the Tangent Line, #25 · Calculus · Derivatives

A light ray comes down the line

A light ray comes down the line $x = a$ . It hits the parabolic reflector $y = x^{2}$ at $P = (a, a^{2})$ .
(a) Find the tangent line at $P$ . Locate the point $Q$ where that line crosses the $y$ axis.
(b) Check that $P$ and $Q$ are the same distance from the focus at $F = (0, \frac{1}{4})$ .
(c) Show from (b) that the figure has equal angles.
(d) What law of physics makes every ray reflect off the parabola to the focus at $F$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.3 The Slope and the Tangent Line, #25

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