JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 31 January 2024, Shift 2, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let

P

be a parabola with vertex

(2,3)

and directrix

2x+y=6

. Let an ellipse

E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b

, of eccentricity

\frac{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) $\frac{512}{25}$
(2) $\frac{385}{8}$
(3) $\frac{656}{25}$ Official answer
(4) $\frac{347}{8}$

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Length of Latus Rectum

Same idea in other shifts

Asked 5× in all

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9 Apr 2024, Shift 1 · Q12Let $f(x)=x^2+9$ , $g(x)=\frac{x}{x-9}$ and $a=f\circ g(10)$ , $b=g\circ f(3)$ . If $e$ and $l$ denote the eccentricity and the length of the…EasySingle correct
31 Jan 2024, Shift 1 · Q28Let the foci and length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b$ be $(\pm5,0)$ and $\sqrt{50}$ ,…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.