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Saturday, 31 October

JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 6 April 2024, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B. NTA dropped this question from the final key; it is left out of every count on this site.

The length of the latus rectum and directrices of a hyperbola with eccentricity ee are 9 and x=±43x=\pm\frac{4}{\sqrt{3}}, respectively. Let the line y−3x+3=0y-\sqrt{3}x+\sqrt{3}=0 touch this hyperbola at (x0,y0)(x_0,y_0). If mm is the product of the focal distances of the point (x0,y0)(x_0,y_0), then 4e2+m4e^2+m is equal to ________.

Official answer

Dropped by NTA (marks given to all)

NTA final key.

Chapter
Conic Sections
Topic
General Conic Section
Idea tested
Focus-Directrix Form Extraction

Same idea in other shifts

Asked 4× in all
  1. 7 Apr 2025, Shift 1 · Q10Let P be the parabola, whose focus is (−2,1)(-2, 1) and directrix is 2x+y+2=02x + y + 2 = 0. Then the sum of the ordinates of the points on P, whose…MediumSingle correct
  2. 25 Jun 2022, Shift 1 · Q19Let x=2tx=2t, y=t23y=\frac{t^2}{3} be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BASA\perp BA, where A…HardSingle correct
  3. 27 Jun 2022, Shift 2 · Q11If the equation of the parabola, whose vertex is at (5,4)(5, 4) and the directrix is 3x+y−29=03x+y-29=0, is x2+ay2+bxy+cx+dy+k=0x^2+ay^2+bxy+cx+dy+k=0, then…MediumSingle correct
  4. 24 Feb 2021, Shift 1 · Q74The locus of the mid-point of the line segment joining the focus of the parabola y2=4axy^2 = 4ax to a moving point of the parabola, is another…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.