Consider the ellipse \frac{x^2}{4}+\frac{y^2}{3}=1 . Let {\H}(\alpha, 0), 0< \alpha< 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 \phi with the positive x-axis. List-1 List-II (I) If \phi=\frac{\pi}{4}, then the area of the triangle F G H is (P) \frac{(\sqrt{3}-1)^4}{8} (II) If \phi=\frac{\pi}{3}, then the area of the triangle F G H is (Q) 1 (III) If \phi=\frac{\pi}{6}, then the area of the triangle F G H is (R) 3/4 (IV) If \phi=\frac{\pi}{12}, then the area of the triangle F G H is (S) \frac{1}{2 \sqrt{3} (T) \frac{3 \sqrt{3}{2} The correct option is: [JEE Adv 2022 P1]

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

( {\I}) \to( {\R}) ;( {\II}) \to( {\S}) ;( {\III}) \to( {\Q}) ;( {\IV}) \to( {\P})

(I) \to( {\R}) ;( {\II}) \to( {\T}) ;( {\III}) \to( {\S}) ;( {\IV}) \to( {\P})

(I) \to( {\Q}) ;( {\II}) \to( {\T}) ;( {\III}) \to( {\S}) ;( {\IV}) \to( {\P})

( {\I}) \to( {\Q}) ;( {\II}) \to( {\S}) ;( {\III}) \to( {\Q}) ;( {\IV}) \to( {\P})

Ellipse

Section: Mathematics

Question : 4 of 25

Marks: +1, -0

Consider the ellipse
‌

+‌

=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.

List-1

List-II

(I)

If φ=‌

, then the area of the triangle FGH is

(P)

‌

(√3−1)4

(II)

If φ=‌

, then the area of the triangle FGH is

(Q)

(III)

If φ=‌

, then the area of the triangle FGH is

(R)

(IV)

If φ=‌

, then the area of the triangle FGH is

(S)

‌

2√3

(T)

‌

3√3

The correct option is:

[JEE Adv 2022 P1]

(I)→(R);(II)→(S);(III)→(Q);(IV)→(P)
(I) →(R);(II)→(T);(III)→(S);(IV)→(P)
(I) →(Q);(II)→(T);(III)→(S);(IV)→(P)
(I)→(Q);(II)→(S);(III)→(Q);(IV)→(P)

Validate

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