JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2026, Shift 2, Maths Q10

Question 10 of 75 in this shift, Maths question 10 of 25, Section A.

Let C be a circle having centre in the first quadrant and touching the

x

-axis at a distance of 3 units from the origin. If the circle C has an intercept of length

6\sqrt{3}

y

-axis, then the length of the chord of the circle C on the line

x-y=3

is :

(1)8
(2)6
(3) $6\sqrt{2}$ Official answer
(4) $8\sqrt{2}$

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Family of Circles Touching a Line

Same idea in other shifts

Asked 4× in all

2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point $(-9, 4)$ and touching the lines…HardNumerical value
25 Jul 2022, Shift 1 · Q29The sum of diameters of the circles that touch (i) the parabola $75x^2=64(5y-3)$ at the point $\left(\frac{8}{5},\frac{6}{5}\right)$ and…HardNumerical value
6 Sep 2020, Shift 2 · Q65The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^2$ at the point $(2,4)$ is :HardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.