JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 June 2022, Shift 1, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let the common tangents to the curves

4(x^2 + y^2) = 9

and

y^2 = 4x

intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and

l

respectively denote the eccentricity and the length of the latus rectum of this ellipse, then

\frac{l}{e^2}

is equal to ________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Common Tangent to Circle and Conic

Same idea in other shifts

Asked 9× in all

10 Apr 2023, Shift 1 · Q29Let a common tangent to the curves $y^2=4x$ and $(x-4)^2+y^2=16$ touch the curves at the points P and Q. Then $(PQ)^2$ is equal to…MediumNumerical value
10 Apr 2023, Shift 2 · Q13Let a circle of radius $4$ be concentric to the ellipse $15x^2 + 19y^2 = 285$ . Then the common tangents are inclined to the minor axis of…HardSingle correct
28 Jul 2022, Shift 2 · Q85Two tangent lines $l_1$ and $l_2$ are drawn from the point (2, 0) to the parabola $2y^2=-x$ . If the lines $l_1$ and $l_2$ are also tangent…HardNumerical value
24 Jun 2022, Shift 1 · Q5Let $x^2+y^2+Ax+By+C=0$ be a circle passing through $(0, 6)$ and touching the parabola $y=x^2$ at $(2, 4)$ . Then $A+C$ is equal to ______.HardSingle correct
25 Jun 2022, Shift 1 · Q16If $y=m_1x+c_1$ and $y=m_2x+c_2$ , $m_1\neq m_2$ are two common tangents of circle $x^2+y^2=2$ and parabola $y^2=x$ , then the value of…HardSingle correct
31 Aug 2021, Shift 2 · Q89A tangent line L is drawn at the point $(2, -4)$ on the parabola $y^2 = 8x$ . If the line L is also tangent to the circle…MediumNumerical value
25 Feb 2021, Shift 2 · Q89A line is a common tangent to the circle $(x-3)^2 + y^2 = 9$ and the parabola $y^2 = 4x$ . If the two points of contact (a, b) and (c, d)…HardNumerical value
26 Feb 2021, Shift 2 · Q90Let L be a common tangent line to the curves $4x^2+9y^2=36$ and $(2x)^2+(2y)^2=31$ . Then the square of the slope of the line L is…HardNumerical value

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.