The points of contact of the vertical tangents to x=2−3 sinθ,  y=3+2 cosθ  are

For vertical tangents dxdθ=0 so, we have −3cos⁡θ=0⇒θ=π2 or 3π2. Corresponding to these  values of θ, we have x=2−3sin⁡π2=−1,y=3+2cos⁡π2=3x=2−3sin⁡3π2=2+3=5,y=3+2cos⁡3π2=3Thus the required points are (-1, 3) ,  (5, 3).