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Question

Two plane mirrors are placed perpendicular to each other and a point object P is placed equidistant from both the mirrors. Find the equation of the geometerical shape at which the images of the object will lie.

A
x2+y2=2
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B
y=x
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C
x+y=2
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D
x2+y2=8
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Solution

The correct option is D x2+y2=8
90 is the angle at which both mirrors are inclined.
So,
n=360θ=36090=4
As n is even, hence, the number of images formed,
=n1=41=3
By symmetry, all the three images and the object will lie on a circle whose centre is at the point of intersection (i.e O) of the mirrors and radius (r) equal to the distance of the object P from the intersection point.
So, r2=22+22=8
[slope is m=tan45=1, so, x=y]


We know the equation of the circle whose centre lie at the origin is given by,
x2+y2=r2, where r is radius.
Thus, here, the equation of the circle is,
x2+y2=8

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