Let T1 and T2 be two distinct... |JEE Advanced 2023| Ellipse

JEE Advance2023

Paper-1 2023

Multiple correct answers - Select all that apply

Question

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

Select ALL correct options:

The area of the quadrilateral $\mathrm{A}_1 \mathrm{~A}_2 \mathrm{~A}_3 \mathrm{~A}_4$ is 35 square units

The area of the quadrilateral $\mathrm{A}_1 \mathrm{~A}_2 \mathrm{~A}_3 \mathrm{~A}_4$ is 36 square units

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

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution