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Consider the ellipse 1 3 y 4 x 2 2 = + 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. List-I List-II (I) If φ = 4 π , then the area of the triangle FGH is (P) 8 ) 1 3 ( 4 − (II) If φ = 3 π , then the area of the triangle FGH is (Q) 1 (III) If φ = 6 π , then the area of the triangle FGH is (R) 4 3 (IV) If φ = 12 π , then the area of the triangle FGH is (S) 3 2 1 (T) 2 3 3 The correct option is :

1. (I) → (R); (II) → (S); (III) → (Q); (IV) → (P)
2. (I) → (R); (II) → (T); (III) → (S); (IV) → (P)
3. (I) → (Q); (II) → (T); (III) → (S); (IV) → (P)
4. (I) → (Q); (II) → (S); (III) → (Q); (IV) → (P)

Correct answer: (I) → (Q); (II) → (T); (III) → (S); (IV) → (P)

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