JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 June 2022, Shift 2, Maths Q29

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

Let the eccentricity of the hyperbola

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

\frac{5}{4}

. If the equation of the normal at the point

\left(\frac{8}{\sqrt{5}}, \frac{12}{5}\right)

on the hyperbola is

8\sqrt{5}x + \beta y = \lambda

, then

\lambda - \beta

is equal to ___________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Normals to Conics
Idea tested: Hyperbola Normal Point Form

Same idea in other shifts

Asked 6× in all

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26 Jun 2022, Shift 2 · Q13The normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{9} = 1$ at the point $(8, 3\sqrt{3})$ on it passes through the point :MediumSingle correct
8 Jan 2020, Shift 2 · Q65If a hyperbola passes through the point $\mathrm{P}(10, 16)$ and it has vertices at $(\pm 6, 0)$ , then the equation of the normal to it at…MediumSingle correct
4 Sep 2020, Shift 1 · Q66Let P(3, 3) be a point on the hyperbola, $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ . If the normal to it at P intersects the $x$ -axis at (9,…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.