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