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Question
If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus.
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Solution
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
y2 = 4ax ...(i)
The point L has the co-ordinates (5, 10) and lies on parabola given by (i).
Substituting x = 5 and y = 10 in (i), we get
102 = 4a (5)
∴ 100 = 20a
∴ a = 5
Focus is at (a, 0), i.e., (5, 0).
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