Learn

Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 February 2021, Shift 2, Maths Q72

Question 72 of 90 in this shift, Maths question 12 of 30, Section A.

A hyperbola passes through the foci of the ellipse x225+y216=1\frac{x^2}{25} + \frac{y^2}{16} = 1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :
  1. (1)x29−y216=1\frac{x^2}{9} - \frac{y^2}{16} = 1Official answer
  2. (2)x29−y24=1\frac{x^2}{9} - \frac{y^2}{4} = 1
  3. (3)x29−y225=1\frac{x^2}{9} - \frac{y^2}{25} = 1
  4. (4)x2−y2=9x^2 - y^2 = 9

Official answer

Option 1

NTA final key.

Chapter
Conic Sections
Topic
Ellipse Eccentricity
Idea tested
Coordinates of foci

Same idea in other shifts

Asked 5× in all
  1. 7 Apr 2025, Shift 2 · Q13Let e1e_1 and e2e_2 be the eccentricities of the ellipse x2b2+y225=1\frac{x^2}{b^2}+\frac{y^2}{25}=1 and the hyperbola…MediumSingle correct
  2. 9 Apr 2024, Shift 2 · Q15Let the foci of a hyperbola HH coincide with the foci of the ellipse E:(x−1)2100+(y−1)275=1E:\frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1 and the eccentricity of…MediumSingle correct
  3. 25 Jul 2022, Shift 2 · Q14Let the foci of the ellipse x216+y27=1\frac{x^2}{16}+\frac{y^2}{7}=1 and the hyperbola x2144−y2α=125\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25} coincide.…MediumSingle correct
  4. 25 Jul 2021, Shift 2 · Q76If a tangent to the ellipse x2+4y2=4x^2+4y^2=4 meets the tangents at the extremities of its major axis at B and C, then the circle with BC as…HardSingle 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.