Problem
Consider the ellipse x²/4 + y²/3 = 1. Let H(α, 0), 0 < α < 2, be a point. A straight line drawn through H parallel to the y-axis crosses the ellipse and its auxiliary circle at points E and F respectively, in the first quadrant. The tangent to the ellipse at the point E intersects the positive x-axis at a point G. Suppose the straight line joining F and the origin makes an angle φ with the positive x-axis.
Match the following.
| List-1 | List-2 |
| (I) If φ = π/4, then the area of the triangle FGH is | (P) (√3 – 1)4/8 |
| (II) If φ = π/3, then the area of the triangle FGH is | (Q) 1 |
| (III) If φ = π/6, then the area of the triangle FGH is | (R) 3/4 |
| (IV) If φ = π/12, then the area of the triangle FGH is | (S) 1/2√3 |
| (T) 3√3/2 |