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Saturday, 31 October

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q13

Question 13 of 75 in this shift, Maths question 13 of 25, Section A.

Let 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 x216−y2b2=1\frac{x^2}{16}-\frac{y^2}{b^2}=1, respectively. If b<5b<5 and e1e2=1e_1e_2=1, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is :
  1. (1)32\frac{\sqrt{3}}{2}
  2. (2)74\frac{\sqrt{7}}{4}
  3. (3)35\frac{3}{5}Official answer
  4. (4)45\frac{4}{5}

Official answer

Option 3

NTA final key.

Chapter
Conic Sections
Topic
Ellipse Eccentricity
Idea tested
Coordinates of foci

Same idea in other shifts

Asked 5× in all
  1. 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
  2. 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
  3. 25 Feb 2021, Shift 2 · Q72A 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…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.