JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Circle

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Let C be a circle having centre in the first quadrant and touching the x -axis at a distance 3 units from the origin. If the circle C has an intercept of length

63

y

-axis, then the length of the chord of the circle

C

on the line

x - y = 3

is :

(A)8
(B)6
(C) $62$ ✓ Correct
(D) $82$

Answer: (C)

Solution

Touching the

x

-axis at

(3, 0)

puts the centre at

(3, r)

with radius

r

. The

y

-axis chord has length

2 r^{2} - 3^{2} = 63

, so

r^{2} - 9 = 27

and

r = 6

; the centre is

(3, 6)

. The distance from

(3, 6)

to the line

x - y - 3 = 0

\frac{∣3 - 6 - 3∣}{2} = 32

, so the chord on this line has length

2 r^{2} - (32)^{2} = 2 36 - 18 = 62

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Single correct option

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