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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 24 June 2022, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let the maximum area of the triangle that can be inscribed in the ellipse x2a2+y24=1\frac{x^2}{a^2} + \frac{y^2}{4} = 1, a>2a > 2, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the yy-axis, be 636\sqrt{3}. Then the eccentricity of the ellipse is:
  1. (1)32\frac{\sqrt{3}}{2}Official answer
  2. (2)12\frac{1}{2}
  3. (3)12\frac{1}{\sqrt{2}}
  4. (4)34\frac{\sqrt{3}}{4}

Official answer

Option 1

NTA final key.

Chapter
Conic Sections
Topic
Ellipse Eccentricity
Idea tested
Maximum Inscribed Rectangle Area via Eccentricity

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.