Let 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 $\sqrt{50}$, respectively. Then, the square of the eccentricity of the hyperbola $\frac{x^2}{b^2}-\frac{y^2}{a^2b^2}=1$ equals ______

JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let the foci and length of the latus rectum of an ellipse

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

(\pm5,0)

and

\sqrt{50}

, respectively. Then, the square of the eccentricity of the hyperbola

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

equals ______

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

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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 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
27 Jul 2022, Shift 1 · Q24An ellipse $E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ passes through the vertices of the hyperbola…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.