Let T_1 and T_2 be two distinct common tangents to the ellipse E : (x^2)/6 + (y^2)/3 = 1 and the parabola P :…

Question

Let T_1 and T_2 be two distinct common tangents to the ellipse E : (x^2)/6 + (y^2)/3 = 1 and the parabola P : y^2 = 12x. Suppose that the tangent T_1 touches P and E at the points A_1 and A_2, respectively and the tangent T_2 touches P and E at the points A_4 and A_3, respectively. Then which of the following statements is(are) true?

Accepted Answer

The area of the quadrilateral A_1 A_2 A_3 A_4 is 35 square units

Accepted Answer

The tangents T_1 and T_2 meet the x-axis at the point (-3, 0)

Answer

The area of the quadrilateral A_1 A_2 A_3 A_4 is 36 square units

Answer

The tangents T_1 and T_2 meet the x-axis at the point (-6, 0)

JEE Advanced 2023 Mathematics question on Conic Sections