Eliminate the parameter in the pair of parametric equations

Eliminate the parameter in the pair of parametric equations and wirte the resulting rectangular equation:

x = sin t

y = 3 cos t

Solution : The given equation may be written as

x=sin t.... (i), y/3 = cos t. ....(ii)

Square both the sides of the equation and add them, to get

x^2 + (y /3)^2= sin^2 t +cos^2 t

Since. sin^2t+cos^2t =1.

Therefore

x^2+ y^2/9 =1. Ans