jee-main 2024 Q68

jee-main · India · session1_31jan_shift2 Conic sections Equation Determination from Geometric Conditions

Let $P$ be a parabola with vertex $(2, 3)$ and directrix $2x + y = 6$. Let an ellipse $E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$, $a > b$ of eccentricity $\dfrac{1}{\sqrt{2}}$ pass through the focus of the parabola $P$. Then the square of the length of the latus rectum of $E$, is
(1) $\dfrac{385}{8}$
(2) $\dfrac{347}{8}$
(3) $\dfrac{512}{25}$
(4) $\dfrac{656}{25}$

Let $P$ be a parabola with vertex $(2, 3)$ and directrix $2x + y = 6$. Let an ellipse $E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$, $a > b$ of eccentricity $\dfrac{1}{\sqrt{2}}$ pass through the focus of the parabola $P$. Then the square of the length of the latus rectum of $E$, is\\
(1) $\dfrac{385}{8}$\\
(2) $\dfrac{347}{8}$\\
(3) $\dfrac{512}{25}$\\
(4) $\dfrac{656}{25}$

Paper Questions

Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73