Let A be area between co-ordinate axes, y 2 = x − 1 , x 2 = y − 1 and the line which makes the shortest distance between two parabolas and A' be the area between x = 0 , x 2 = y − 1 x = y and sho

Question

Let A be area between co-ordinate axes, y 2 = x − 1 , x 2 = y − 1 and the line which makes the shortest distance between two parabolas and A' be the area between x = 0 , x 2 = y − 1 x = y and shortest segment between y 2 = x − 1 and x 2 = y − 1 then -

TestHub · Accepted Answer

Given curves are y 2 = x − 1 , x 2 = y − 1 These two are inverse of each other through line y = x Given Area of region OPQ : A & Area of region OPR : A ′ In this case R is midpoint of line PQ So A = 2 A ′ Reflection in y=x swaps the two halves of the bounded region. Hence A=2A'.

Mathematics - Area Under Curves Question with Solution | TestHub

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