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Area enclosed by the curve y=f(x) define...

Area enclosed by the curve `y=f(x)` defined parametrically as `x=(1-t^2)/(1+t^2),y=(2t)/(1+t^2)i se q u a lto` `pis qdotu n i t s` (b) `pi/2s qdotu n i t s` `(3pi)/4s qdotu n i t s` (d) `(3pi)/2s qdotu n i t s`

A

`pi` sq. units

B

`pi//2` sq. units

C

`(3pi)/(4)` sq. units

D

`(3pi)/(2)` sq. units

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly t can be any real number
`"Let "t=tan theta rArr x=(1-tan^(2)theta)/(1+tan^(2)theta)`
`rArr" "x=cos 2theta and y =(2 tan theta)/(1+tan^(2)theta)=sin 2theta`
`rArr" "x^(2)+y^(2)=1`
Thus, required area is `pi` sq. units.
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