JEE Main 2026 · 6 Apr · Shift 2 · Mathematics Q10

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MathematicsSingle correct+4 / -1Question 10 of 75

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 $6\sqrt3$ on $y$ -axis, then the length of the chord of the circle C on the line $x-y=3$ is :

6\sqrt2

8\sqrt2

Answer and worked solution

Official answer: C

Centre. Touching the x-axis at $(3,0)$ : centre $(3,r)$ .

Radius. y-intercept $2\sqrt{r^2-9}=6\sqrt3$ , so $r=6$ .

Chord on $x-y=3$ . Distance from $(3,6)$ is $\dfrac{|3-6-3|}{\sqrt2}=3\sqrt2$ , so
$\text{chord}=2\sqrt{36-18}=6\sqrt2.$

(C)

Topics:Equation of a circle

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JEE Main 2026 · 6 Apr · Shift 2, Mathematics question 10