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Question

A ray of light parallel to yāˆ’axis is incident on a parabola y=4x2 polished from inside as shown in the figure. Find the co-ordinates x and y of the point at which the incident ray should fall such that the reflected ray becomes horizontal after reflection.

A
(x,y)=(116,164)
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B
(x,y)=(18,116)
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C
(x,y)=(12,14)
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D
(x,y)=(14,18)
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Solution

The correct option is B (x,y)=(18,116)
The given situation can be shown as below
From the geometry we can say that the slope of the parabola at the point (x,y) should be tan45
Given, y=4x2
slope,dydx=8x=tan45=1
x=18, putting value of x in the equation of parabola, we will get
y=4×(18)2=116
Thus, (x,y)=(18,116)

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