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Q.
If a parabolic reflector is $20 \,cm$ in diameter and $5 \,cm$ deep, then the focus is
Conic Sections
Solution:
Taking vertex of the parabolic reflector at origin, x-axis along the axis of parabola. The equation of the parabola is $y ^{2}=4 ax$. Given depth is $5 cm$, diameter is $20 \,cm$
$\because$ Point $P (5,10)$ lies on parabola.
$\therefore (10)^{2}=4 a(5) $
$\Rightarrow a=5$
Clearly, focus is at the mid-point of given diameter.
i.e., $S = (5, 0)$
