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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

Let E1:x2a2+y2b2=1\mathrm{E}_1:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>ba>b. Let E2\mathrm{E}_2 be another ellipse such that it touches the end points of major axis of E1\mathrm{E}_1 and the foci of E2\mathrm{E}_2 are the end points of minor axis of E1\mathrm{E}_1. If E1\mathrm{E}_1 and E2\mathrm{E}_2 have same eccentricities, then its value is :
  1. (1)−1+52\frac{-1+\sqrt{5}}{2}Official answer
  2. (2)−1+82\frac{-1+\sqrt{8}}{2}
  3. (3)−1+62\frac{-1+\sqrt{6}}{2}
  4. (4)−1+32\frac{-1+\sqrt{3}}{2}

Official answer

Option 1

NTA final key.

Chapter
Conic Sections
Topic
Ellipse Eccentricity
Idea tested
Similarity of Ellipses

Same topic in other shifts

All Ellipse Eccentricity questions
  1. 2 Apr 2026, Shift 1 · Q10Let an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a<ba<b, pass through the point (4,3)(4, 3) and have eccentricity 53\frac{\sqrt5}{3}. Then…MediumSingle correct
  2. 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
  3. 5 Apr 2026, Shift 1 · Q9Let a focus of the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 be S(4,0)S(4, 0) and its eccentricity be 45\frac{4}{5}. If the point…EasySingle correct
  4. 8 Apr 2026, Shift 2 · Q2The number of values of z∈Cz \in \mathbb{C}, satisfying the equations ∣z−(4+8i)∣=10|z - (4 + 8i)| = \sqrt{10} and…HardSingle correct
  5. 2 Apr 2025, Shift 1 · Q4If S and S' are the foci of the ellipse x218+y29=1\frac{x^2}{18}+\frac{y^2}{9}=1 and P be a point on the ellipse, then…MediumSingle correct
  6. 2 Apr 2025, Shift 2 · Q12If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the…EasySingle 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.