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If a parabolic reflector is $20 \mathrm{~cm}$ in diameter and $5 \mathrm{~cm}$ deep, find the focus.
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Taking vertex of the parabola reflector at origin, $x$-axis along the axis of parabola the equation of parabola is $y^2=4 a x$. Given depth $5 \mathrm{~cm}$, diameter $20 \mathrm{~cm}$
$\therefore(5,10)$ point lies on parabola
$\begin{aligned}(10)^2 &=4 a(5) \\ \therefore a &=5 \end{aligned}$
$\therefore$ Focus is $(a, 0)$, i.e. $(5,0)$ which is mid-point of the given diameter
$\therefore(5,10)$ point lies on parabola
$\begin{aligned}(10)^2 &=4 a(5) \\ \therefore a &=5 \end{aligned}$
$\therefore$ Focus is $(a, 0)$, i.e. $(5,0)$ which is mid-point of the given diameter
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