JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 1 February 2024, Shift 2, Maths Q13

Question 13 of 90 in this shift, Maths question 13 of 30, Section A.

Let

P

be a point on the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

. Let the line passing through

P

and parallel to

y

-axis meet the circle

x^2+y^2=9

at point

Q

such that

P

and

Q

are on the same side of the

x

-axis. Then, the eccentricity of the locus of the point

R

PQ

such that

PR:RQ=4:3

P

moves on the ellipse, is :

(1) $\frac{\sqrt{13}}{7}$ Official answer
(2) $\frac{11}{19}$
(3) $\frac{\sqrt{139}}{23}$
(4) $\frac{13}{21}$

Official answer

Option 1

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Eccentricity calculation

Same idea in other shifts

Asked 11× in all

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1 Feb 2024, Shift 1 · Q12For $0<\theta<\pi/2$ , if the eccentricity of the hyperbola $x^2-y^2\mathrm{cosec}^2\theta=5$ is $\sqrt{7}$ times eccentricity of the…MediumSingle correct
6 Apr 2023, Shift 2 · Q2In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of…EasySingle correct
25 Jul 2022, Shift 2 · Q12If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2\sqrt{6}}=1$ on the $x$ -axis and the line…EasySingle correct
27 Jun 2022, Shift 1 · Q13Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a>b$ , be $\frac{1}{4}$ . If this ellipse passes through the point…EasySingle correct
30 Jun 2022, Shift 1 · Q15Let the eccentricity of the ellipse $x^2 + a^2y^2 = 25a^2$ be b times the eccentricity of the hyperbola $x^2 - a^2y^2 = 5$ , where a is the…HardSingle correct
25 Jul 2021, Shift 1 · Q61Let an ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a^2>b^2$ , passes through $\left(\sqrt{\frac{3}{2}},1\right)$ and has eccentricity…HardSingle correct
9 Jan 2020, Shift 1 · Q66If $\mathrm{e}_1$ and $\mathrm{e}_2$ are the eccentricities of the ellipse, $\frac{x^2}{18}+\frac{y^2}{4}=1$ and the hyperbola,…EasySingle correct

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 108 of the 174 JEE Main shifts held from 2017 to 2026.