Consider the ellipse x²/4+y²/3=1. Let H(α,0), 0<α<2. A vertical line through H crosses the ellipse and its auxiliary circle at E and F respectively, in the first quadrant. The tangent to the ellipse at E intersects the positive x-axis at G. The line joining F to the origin makes angle φ with the positive x-axis. Match List-I: (I) φ=π/4; (II) φ=π/3; (III) φ=π/6; (IV) φ=π/12, for the area of triangle FGH, with List-II: (P)(√3−1)⁴/8; (Q)1; (R)3/4; (S)1/(2√3); (T)3√3/2.