JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 1 February 2024, Shift 1, Maths Q15

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

Let

C: x^2+y^2=4

and

C': x^2+y^2-4\lambda x+9=0

be two circles. If the set of all values of

\lambda

so that the circles C and C' intersect at two distinct points, is

\mathbb{R}-[a,b]

, then the point

(8a+12, 16b-20)

lies on the curve :

(1) $5x^2-y=-11$
(2) $6x^2+y^2=42$ Official answer
(3) $x^2-4y^2=7$
(4) $x^2+2y^2-5x+6y=3$

Official answer

Option 2

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Number of Common Tangents

Same idea in other shifts

Asked 6× in all

15 Apr 2023, Shift 1 · Q13The number of common tangents, to the circles $x^2+y^2-18x-15y+131=0$ and $x^2+y^2-6x-6y-7=0$ , isEasySingle correct
17 Mar 2021, Shift 1 · Q75Choose the incorrect statement about the two circles whose equations are given below : $x^{2}+y^{2}-10x-10y+41=0$ and…MediumSingle correct
17 Mar 2021, Shift 1 · Q86The minimum distance between any two points $P_1$ and $P_2$ while considering point $P_1$ on one circle and point $P_2$ on the other…EasyNumerical value
18 Mar 2021, Shift 1 · Q75Choose the correct statement about two circles whose equations are given below : $x^2+y^2-10x-10y+41=0$ $x^2+y^2-22x-10y+137=0$ EasySingle correct
9 Jan 2020, Shift 2 · Q73If the curves, $x^2-6x+y^2+8=0$ and $x^2-8y+y^2+16-k=0$ , $(k>0)$ touch each other at a point, then the largest value of $k$ is ______.MediumNumerical 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.