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 y-axis crosses the ellipse and its auxiliary circle at points E and F respectively, in the first quadrant. The tangents 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 = π/4 , then the area of the triangle FGH is |
(P) |
\(\frac{(\sqrt{3}-1)^4}{8}\) |
| (II) |
If ϕ = π/4, 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) |
\(\frac{1}{2\sqrt{3}}\) |
|
|
(T) |
\(\frac{3\sqrt{3}}{2}\) |
The correct option is:
(A) (I) → (R); (II) → (S); (III) → (Q); (IV) → (P)
(B) (I) → (R); (II) → (T); (III) → (S); (IV) → (P)
(C) (1)→(Q); (II) → (T); (III) → (S); (IV) → (P)
(D) (I) → (Q); (II) → (S); (III) → (Q); (IV) → (P)
