Home
Class 12
MATHS
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))` is equal to

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.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • AREA

    CENGAGE|Exercise Exercise (Multiple)|10 Videos

  • AREA

    CENGAGE|Exercise Exercise (Comprehension)|21 Videos

  • AREA

    CENGAGE|Exercise Exercise 9.3|7 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE|Exercise Question Bank|29 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) , then dy/dx is equal to

If x=a((1+t^(2))/(1-t^(2))) and y=(2t)/(1-t^(2)), find (dy)/(dx)

Knowledge Check

  • Consider the parametric equation x=(a(1-t^(2)))/(1+t^(2))" and "y=(2at)/(1+t^(2)) What is (dy)/(dx) equal to ?

    A
    `y//x`
    B
    `-y//x`
    C
    `x//y`
    D
    `-x//y`

  • If x=(1-t^(2))/(1+t^(2)) and y=(2t)/(1+t^(2)) , then (dy)/(dx) is equal to

    A
    `-(y)/(x)`
    B
    `(y)/(x)`
    C
    `-(x)/(y)`
    D
    `(x)/(y)`

  • The conic having parametric representation x=sqrt3((1-t^(2)/(1+t^(2))),y(=2t)/(1+t^(2)) is

    A
    an circle
    B
    a parabola
    C
    an ellipse
    D
    a hyperbola

    • Similar Questions

    Explore conceptually related problems

    If x=a((1+t^(2))/(1-t^(2))) and y=(2t)/(1-t^(2)), find (dy)/(dx)

    The curve described parametrically by x=t^(2)+t+1,y=t^(2)-t+1 represents :

    The locus of the point x=(t^(2)-1)/(t^(2)+1),y=(2t)/(t^(2)+1)

    The eccentricity of the conic x=3((1-t^(2))/(1+t^(2))) and y=(2t)/(1+t^(2)) is

    If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2) ,then (dy)/(dx)=

    Home
    Profile