JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q29

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

A common tangent T to the curves

C_1 : \frac{x^2}{4} + \frac{y^2}{9} = 1

and

C_2 : \frac{x^2}{42} - \frac{y^2}{143} = 1

does not pass through the fourth quadrant. If T touches

C_1

(x_1, y_1)

and

C_2

(x_2, y_2)

, then

|2x_1 + x_2|

is equal to __________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Tangents and Normals
Idea tested: Common Tangents to Two Curves

Same idea in other shifts

Asked 4× in all

26 Jul 2022, Shift 2 · Q12The equation of a common tangent to the parabolas $y=x^2$ and $y=-(x-2)^2$ isMediumSingle correct
29 Jul 2022, Shift 2 · Q27If the tangent to the curve $y=x^3-x^2+x$ at the point $(a, b)$ is also tangent to the curve $y=5x^2+2x-25$ at the point $(2,-1)$ , then…MediumNumerical value
26 Jun 2022, Shift 2 · Q11If $m$ is the slope of a common tangent to the curves $\frac{x^2}{16} + \frac{y^2}{9} = 1$ and $x^2 + y^2 = 12$ , then $12\, m^2$ is equal…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.