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A-mirror-is-designed-so-that-any-ray-of-light-which-hits-one-side-of-the-mirror-and-which-is-parallel-to-a-certain-fixed-line-L-is-reflected-through-a-fixed-point-O-Prove-that-the-mirror-intersects-




Question Number 2129 by Yozzi last updated on 03/Nov/15
A mirror is designed so that any ray  of light which hits one side of the  mirror and which is parallel to a   certain fixed line L is reflected through  a fixed point O. Prove that the mirror  intersects any plane containing L in  a parabola.  I would appreciate a formal proof.
$${A}\:{mirror}\:{is}\:{designed}\:{so}\:{that}\:{any}\:{ray} \\ $$$${of}\:{light}\:{which}\:{hits}\:{one}\:{side}\:{of}\:{the} \\ $$$${mirror}\:{and}\:{which}\:{is}\:{parallel}\:{to}\:{a}\: \\ $$$${certain}\:{fixed}\:{line}\:{L}\:{is}\:{reflected}\:{through} \\ $$$${a}\:{fixed}\:{point}\:{O}.\:{Prove}\:{that}\:{the}\:{mirror} \\ $$$${intersects}\:{any}\:{plane}\:{containing}\:{L}\:{in} \\ $$$${a}\:{parabola}. \\ $$$${I}\:{would}\:{appreciate}\:{a}\:{formal}\:{proof}. \\ $$$$ \\ $$

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