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`

Options

A. `pi` sq. units
B. `pi//2` sq. units
C. `(3pi)/(4)` sq. units
D. `(3pi)/(2)` sq. units

Answer

A

Explanation

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.