If the co-ordinates of a variable point P be (acostheta,bsintheta) where theta is a variable quantity, find the locus of P. Share with your friends Share 20 Anuradha Sharma answered this The coordinates of variable point P is acos θ,bsin θ.Let the coordinate be x,y so, x=acos θor cos θ=xa.......1and y =bsin θso sin θ=yb........2Now squaring both the equation 1 and 2 and adding we get, sin2 θ+cos2 θ=xa2+yb2or x2a2+y2b2=1And this the equation of ellipse. so the locus of P is a ellipse. 92 View Full Answer