(x2∕9)+(y2∕4)=1 Using parametric coordinate of the ellipse (a‌cos‌θ,b‌sin‌θ)=(3‌cos‌θ,2‌sin‌θ)
Equation of tangent at point (3‌cos‌θ,2‌sin‌θ) is T=0{T=xx1∕a2+yy1∕b2=1} PQ:[3x‌cos‌θ∕9]+[2y‌sin‌θ∕4]=1 PQ:[x‌cos‌θ∕3]+[y‌sin‌θ∕2]=1 At x=0⇒y=2cosecθ At y=0⇒x=3‌sec‌θ Area of quadrilateral A(θ)=4× Area of △OPQ =4×(1∕2)× Base (OP) × Height (OQ) =4×(1∕2)×3‌sec‌θ‌.2‌cosec‌θ =12∕[sin‌θ‌cos‌θ] =24∕sin‌2‌θ Minimum A(θ)=24∕(sin‌2‌θ)max=24∕1=24