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
A=A′
A=A′1/2
A=2A′
can't say anything
Line of shortest distance will be perpendicular to line x=y. Also both parabolas are symmetric about x = y
A= area OABCDOA′=area OECDO⇒A′=A/2