Question
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus.
✓
Answer
Let LOM be the parabolic reflector such that LM is the diameter and ON is its depth.
It is given that ON = 5 cm and LM = 20 cm.
LN = 10 cm Taking O as the origin,
ON along X-axis and a line through O ⊥ ON as Y-axis.
Let the equation of the reflector be $y^2=4 a x \ldots \ldots$ (i)
Substituting $x=5$ and $y=10$ in (i), we get
$\begin{aligned} & \Rightarrow 10^2=4 a(5) \\ & \Rightarrow 100=20 a \\ & \Rightarrow a=5\end{aligned}$
Focus is at (a, 0), i.e., (5, 0)
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