Let the tangent at A(p,q) to the ellipse x216+y24=1 form a triangle of least area with the coordinate axes (p,q>0) .
Then p2+q2 is equal to
T:x4cosθ+y2sinθ=1 Area =12(4secθ)(2cosecθ) Area =8sin2θ For area to be least θ=π4 . ∴p=22 and q=2∴p2+q2=8+2=10