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Saturday, 31 October

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

An ellipse E:x2a2+y2b2=1E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 passes through the vertices of the hyperbola H:x249−y264=−1H : \dfrac{x^2}{49} - \dfrac{y^2}{64} = -1. Let the major and minor axes of the ellipse EE coincide with the transverse and conjugate axes of the hyperbola HH, respectively. Let the product of the eccentricities of EE and HH be 12\dfrac{1}{2}. If ll is the length of the latus rectum of the ellipse EE, then the value of 113l113l is equal to ________.

Official answer

1552

NTA final key.

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

Same idea in other shifts

Asked 12× in all
  1. 4 Apr 2026, Shift 1 · Q22Consider the parabola P:y2=4kxP: y^2=4kx and the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1. Let the line segment joining the points of…MediumNumerical value
  2. 7 Apr 2025, Shift 2 · Q12Let the length of a latus rectum of an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 be 10. If its eccentricity is the minimum value of the…MediumSingle correct
  3. 5 Apr 2024, Shift 1 · Q15Let the line 2x+3y−k=02x+3y-k=0, k>0k>0, intersect the xx-axis and yy-axis at the points A and B, respectively. If the equation of the circle…MediumSingle correct
  4. 9 Apr 2024, Shift 1 · Q12Let f(x)=x2+9f(x)=x^2+9, g(x)=xx−9g(x)=\frac{x}{x-9} and a=f∘g(10)a=f\circ g(10), b=g∘f(3)b=g\circ f(3). If ee and ll denote the eccentricity and the length of the…EasySingle correct
  5. 1 Feb 2024, Shift 1 · Q13Let x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>ba>b be an ellipse, whose eccentricity is 12\frac{1}{\sqrt{2}} and the length of the latusrectum…MediumSingle correct
  6. 31 Jan 2024, Shift 1 · Q28Let the foci and length of the latus rectum of an ellipse x2a2+y2b2=1, a>b\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b be (±5,0)(\pm5,0) and 50\sqrt{50},…MediumNumerical value
  7. 31 Jan 2024, Shift 2 · Q14Let PP be a parabola with vertex (2,3)(2,3) and directrix 2x+y=62x+y=6. Let an ellipse E:x2a2+y2b2=1, a>bE:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b, of…HardSingle correct
  8. 6 Apr 2023, Shift 2 · Q27Let the eccentricity of an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 is reciprocal to that of the hyperbola 2x2−2y2=12x^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.