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If the equation of one tangent to the circle with centre at $(2,-1)$ from the origin is $3 x+y=0$, then the equation of the other tangent through the origin is
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Verified Answer
The correct answer is:
$x-3 y=0$
$$
\begin{aligned}
&\because \mathrm{CA}=\mathrm{CB} \\
&\Rightarrow \frac{5}{\sqrt{10}}=\left|\frac{2 \mathrm{~m}+1}{\sqrt{1+\mathrm{m}^2}}\right|
\end{aligned}
$$
squaring
$$
\frac{25}{10}=\frac{4 m^2+4 m+1}{1+m^2}
$$
$$
\Rightarrow 5+5 m^2=8 m^2+8 m+2 \Rightarrow 3 m^2+8 m-3=0 \Rightarrow m=\frac{1}{3},-3
$$
$\therefore$ Equation of tangent $\mathrm{OB}$ is $y=\frac{x}{3}$
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