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Saturday, 31 October

JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 30 January 2024, Shift 2, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Consider two circles C1:x2+y2=25C_1: x^2 + y^2 = 25 and C2:(x−α)2+y2=16C_2: (x - \alpha)^2 + y^2 = 16, where α∈(5,9)\alpha \in (5, 9). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C1C_1 and C2C_2 be sin⁡−1(638)\sin^{-1}\left(\frac{\sqrt{63}}{8}\right). If the length of common chord of C1C_1 and C2C_2 is β\beta, then the value of (αβ)2(\alpha\beta)^2 equals ________.

Official answer

1575

NTA final key.

Chapter
Conic Sections
Topic
Power of a Point
Idea tested
Length of Common Chord via Radical Axis

Same idea in other shifts

Asked 3× in all
  1. 28 Jun 2022, Shift 2 · Q23If one of the diameters of the circle x2+y2−22x−62y+14=0x^2+y^2-2\sqrt{2}x-6\sqrt{2}y+14=0 is a chord of the circle…MediumNumerical value
  2. 3 Sep 2020, Shift 2 · Q64Let the latus ractum of the parabola y2=4xy^2 = 4x be the common chord to the circles C1C_1 and C2C_2 each of them having radius 252\sqrt{5}.…MediumSingle 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.