JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 24 June 2022, Shift 1, Maths Q15

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

Let

\lambda x-2y=\mu

be a tangent to the hyperbola

a^2x^2-y^2=b^2

. Then

\left(\frac{\lambda}{a}\right)^2-\left(\frac{\mu}{b}\right)^2

is equal to :

(1) $-2$
(2) $-4$
(3)2
(4)4Official answer

Official answer

Option 4

NTA final key (2022 Session 1).

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Condition for Line to be Tangent

Same idea in other shifts

Asked 7× in all

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3 Aug 2021, Shift 1 · Q73If the line $\alpha x + \beta y = 1$ touches the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ , then the locus of the point…MediumSingle correct
22 Jul 2021, Shift 2 · Q68Let a line $\mathrm{L}:2x+y=k$ , $k>0$ be a tangent to the hyperbola $x^2-y^2=3$ . If $\mathrm{L}$ is also a tangent to the parabola…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.