JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 28 July 2022, Shift 1, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

For the hyperbola

H:x^2-y^2=1

and the ellipse

E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b>0

, let the (1) eccentricity of E be reciprocal of the eccentricity of H, and (2) the line

y=\sqrt{\frac{5}{2}}x+K

be a common tangent of E and H. Then

4(a^2+b^2)

is equal to __________.

Official answer

NTA final key (2022 Session 2).

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

Same idea in other shifts

Asked 5× in all

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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 42 of the 174 JEE Main shifts held from 2017 to 2026.