JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 24 June 2022, Shift 2, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let the hyperbola

H : \frac{x^2}{a^2} - y^2 = 1

and the ellipse

E : 3x^2 + 4y^2 = 12

be such that the length of latus rectum of

H

is equal to the length of latus rectum of

E

. If

e_H

and

e_E

are the eccentricities of

H

and

E

respectively, then the value of

12\left(e_H^2 + e_E^2\right)

is equal to ____.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 12× in all

4 Apr 2026, Shift 1 · Q22Consider the parabola $P: y^2=4kx$ and the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ . Let the line segment joining the points of…MediumNumerical value
7 Apr 2025, Shift 2 · Q12Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be 10. If its eccentricity is the minimum value of the…MediumSingle correct
5 Apr 2024, Shift 1 · Q15Let the line $2x+3y-k=0$ , $k>0$ , intersect the $x$ -axis and $y$ -axis at the points A and B, respectively. If the equation of the circle…MediumSingle correct
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
1 Feb 2024, Shift 1 · Q13Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a>b$ be an ellipse, whose eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latusrectum…MediumSingle 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
31 Jan 2024, Shift 2 · Q14Let $P$ 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…HardSingle correct
6 Apr 2023, Shift 2 · Q27Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is reciprocal to that of the hyperbola $2x^2-2y^2=1$ . If the…HardNumerical 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 108 of the 174 JEE Main shifts held from 2017 to 2026.