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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 13 April 2023, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let the tangent and normal at the point (33,1)(3\sqrt{3},1) on the ellipse x236+y24=1\frac{x^2}{36}+\frac{y^2}{4}=1 meet the yy-axis at the points AA and BB respectively. Let the circle CC be drawn taking ABAB as a diameter and the line x=25x=2\sqrt{5} intersect CC at the points PP and QQ. If the tangents at the points PP and QQ on the circle intersect at the point (α,β)(\alpha,\beta), then α2−β2\alpha^2-\beta^2 is equal to
  1. (1)6060
  2. (2)6161
  3. (3)3045\frac{304}{5}Official answer
  4. (4)3145\frac{314}{5}

Official answer

Option 3

NTA final key.

Chapter
Conic Sections
Topic
Circle Tangents
Idea tested
Equation of Polar

Same topic in other shifts

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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.