If A32,2,B-32,2,C-32,-2 and D(3cosθ,2sinθ) are four points. If  the area of quadrilateral ABCD is maximum  where θ∈3π2,2π , then

Area of quadrilateral ABCD is maximum when area of ACD is maximum Distance of D from AC 2x-3y=0 is maximum  i.e., cosθ-sinθ is maximum =2cosθ+π4 is maximum ⇒θ=7π4 and area =62·22=12 sq.units (since ABCD is a rectangle)