If $3x+y=0$ tangent to the circle having its centre at (2, -1), then the equation of other tangent to the circle from the origin, is

Let y = mx be a tangent drawn from the origin to the circle having its centre at (2, -1) and touching $3x+y=0$

Then,

$\begin{array}{l}\left|\frac{2m+1}{\sqrt{m^2+1}}\right|=\left|\frac{6-1}{\sqrt{9+1}}\right|\\ \Rightarrow 2(2m+1{)}^2=5\left(m^2+1\right)\\ \Rightarrow 3m^2+8m-3=0\Rightarrow (3m-1)(m+3)=0\Rightarrow m=-3,\frac{1}{3}\end{array}$

Thus, the equation of the tangents drawn from the origin are

$y=-3x\text{ and }y=x/3$