If the coordinates of avariable point P be (acostheta,bsintheta) whre theta is variable quantity , find the locus of P.

P(x,y)=p(a cos theta,b sin theta ) X=a cos theta y= b sin theta X/a = cos theta y/b sin theta Squaring on both sides X^2/a^2= cos ^2theta y^2/b^2=sin^2theta Adding both X^2/a^2 +y^2/b^2 =1Hence proved

X=acostheta ; Y=bsinthetaX/a=cos there; Y/b=bsinthetaSquaring both the equationsX^2 /a^2=cos^2theta;y^2/b^2=sin^2 thetaAdding both equationsX^2b^2+y^2a^2=a^2b^2. (Cos^2theta +sin^2theta=1)