Conic Sections · JEE Main previous year questions

2024 26 questions

1. Q82024 · 27 Jan 2024 · Shift 2

   Let $e_1$ be the eccentricity of the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $e_2$ be the eccentricity of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a>b$, which passes through the foci of the hyperbola. If $e_1{e}_2=1$, then the length of the chord of the ellipse parallel to the $x$-axis and passing through $(0,2)$ is :

   1. A.$\frac{8\sqrt{5}}{3}$
   2. B.$3\sqrt{5}$
   3. C.$4\sqrt{5}$
   4. D.$\frac{10\sqrt{5}}{3}$
   Show answer

   Answer: D