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

Question

Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + 2 = 0. Then the length of the chord, of the circle C, whose mid-point is (1, 2), is:

Accepted Answer

$$\begin{aligned}
&\begin{aligned}
& \mathrm{M}_{A B}=0 \Rightarrow \mathrm{OM} \text { is vertical } \
& \Rightarrow \alpha=2 \
& \therefore \text { Centre }(0) \equiv(2,-4) \
& \quad r=O A=\sqrt{(2-4)^2+(2+4)^2}=\sqrt{40}
\end{aligned}\
\&\text { mid point of chord is } \mathrm{N} \equiv(1,2) \quad \therefore \mathrm{ON}=\sqrt{37}\
\&\begin{aligned}
\therefore \text { length of chord } & =2 \sqrt{\mathrm{r}^2-(\mathrm{ON})^2} \
& =2 \sqrt{40-37}=2 \sqrt{3}
\end{aligned}
\end{aligned}$$

Solutions · 1