JEE Advanced 2022 Mathematics question

Consider the ellipse

+ = 1.

Let , , be a point. A straight line drawn through parallel to the -axis crosses the ellipse and its auxiliary circle at points and respectively, in the first quadrant. The tangent to the ellipse at the point intersects the positive -axis at a point . Suppose the straight line joining and the origin makes an angle with the positive -axis. List-I (I) If , then the area of the triangle is (II) If , then the area of the triangle is (III) If , then the area of the triangle is (IV) If , then the area of the triangle is List-II (P) (Q) 1 (R) (S) (T) The correct option is:

• (A)(I) → (R); (II) → (S); (III) → (Q); (IV) → (P)
• (B)(I) → (R); (II) → (T); (III) → (S); (IV) → (P)
• (C)(I) → (Q); (II) → (T); (III) → (S); (IV) → (P)Correct
• (D)(I) → (Q); (II) → (S); (III) → (Q); (IV) → (P)