Mathematics · Circles

JEE Main 2025 — 29 January, Evening Shift — Question 55

Let a circle $C$ pass through the points $(4,2)$ and $(0$ , 2 ), and its centre lie on $3 x+2 y+2=0$ .

Then the length of the chord, of the circle C , whose midpoint is $(1,2)$ , is

Answer: B

$\mathrm{M}_{\mathrm{AB}}=0 \Rightarrow \mathrm{OM}$ is vertical

$\Rightarrow \alpha=2$

$\therefore$ Centre $(0) \equiv(2,-4)$

\mathrm{r}=\mathrm{OA}=\sqrt{(2-4)^{2}+(2+4)^{2}}=\sqrt{40}

mid point of chord is $\mathrm{N} \equiv(1,2) \quad \therefore \mathrm{ON}=\sqrt{37}$

$\therefore$ length of chord $=2 \sqrt{\mathrm{r}^{2}-(\mathrm{ON})^{2}}$

=2 \sqrt{40-37}=2 \sqrt{3}

Answer key and solution verified before publishing.

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.