Question

1. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus

JEE/Engineering Exams

Maths

Solution

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This is a parabola of the form ( y^{2}=4 a x, ) as it opens to the right. It passes through the point ( (10,5) rightarrow 10^{2}=4 times a times 5 rightarrow 100=20 a rightarrow a=5 ) Therefore, the focus ( =(a, 0)=(5,0) ). This is the mid-point of the diameter.