Let A be the area between co-ordinate axis, y2=x−1,x2=y−1 and the line which makes the shortest distance between two parabolas and A′ be the area between x=0,x2=y−1,x=y and the shortest distance between y2=x−1 and x2=y−1, then

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A=A′

A=A′1/2

A=2A′

can't say anything

answer is C.

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Detailed Solution

Line of shortest distance will be perpendicular to line x=y. Also both parabolas are symmetric about x = yA= area OABCDOA′=area OECDO⇒A′=A/2

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