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Saturday, 31 October

JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 July 2022, Shift 1, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let the function f(x)=2x2−log⁡exf(x) = 2x^2 - \log_e x, x>0x > 0, be decreasing in (0, a)(0,\ \mathrm{a}) and increasing in (a, 4)(\mathrm{a},\ 4). A tangent to the parabola y2=4axy^2 = 4\mathrm{a}x at a point P on it passes through the point (8a, 8a−1)(8\mathrm{a},\ 8\mathrm{a} - 1) but does not pass through the point (−1a, 0)\left(-\frac{1}{\mathrm{a}},\ 0\right). If the equation of the normal at P is xα+yβ=1\frac{x}{\alpha} + \frac{y}{\beta} = 1, then α+β\alpha + \beta is equal to __________.

Official answer

45

NTA final key.

Chapter
Application of Derivatives
Topic
Normals to Conics
Idea tested
Parabola Normal Point Form

Same idea in other shifts

Asked 2× in all
  1. 27 Aug 2021, Shift 1 · Q70A tangent and a normal are drawn at the point P(2,−4)P(2, -4) on the parabola y2=8xy^2=8x, which meet the directrix of the parabola at the points…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.