Mathematics · Circles

JEE Main 2026 — 6 April, Evening Shift — Question 29

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

Option A:
$8$
Option B:
$6$
Option C:
$6\sqrt2$
Correct
Option D:
$8\sqrt2$

Answer: C

Step-by-step solution

Centre of circle is $(3,6)$ and radius $=6$ units.

\begin{aligned} & P Q=2 \sqrt{6^{2}-p^{2}} \therefore p=\frac{6}{\sqrt{2}} \\& p=\frac{|3-6-3|}{\sqrt{2}} \\& P Q=2 \sqrt{36-\frac{36}{2}} \\& =2 \times \frac{6}{\sqrt{2}}=6 \sqrt{2} \end{aligned}

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Exam: JEE Main 2026
Paper: 6 April, Evening Shift
Subject: Mathematics
Chapter: Circles
Topic: Introduction to Circles

Let the line x-y=4 intersect the circle C: (x-4)²+(y+3)²=9 at the points Q and R. If P(α,β) is a point on C such that PQ=PR, then (6α+8β)²…

Answer: C

Step-by-step solution

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