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Question
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.
Solution
The diameter of the parabolic reflector, AOB,
AB = 20 cm
and AM = 10 cm
deep of reflector, OM = 5 cm
If OX, OY are the coordinate axis then the point lies on the parabola.
Let the equation of parabola be, y2 = 4ax
∴ 102 = 4a × 5
= 100 = 20a
a = `100/20`
∴ a = 5
The focus of the parabola is (a, 0) or (5, 0).
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