Find equation tangent to the circle from origin

Question

If 3x+y=0 is a tangent to the circle with centre at the point (2,-1) , then the equation of the other tangent to the circle from the origin is what ??

Answer 1

Hint:

If $mx-y=0$ is the other tangent

$$\dfrac{|3(2)+1(-1)|}{\sqrt{3^2+1^2}}=\dfrac{|m(2)+(-1)(-1)|}{\sqrt{1^2+m^2}}$$ both being equal to radius

Answer 2

Hint: The two tangents are symmetric about the line through the circle’s center and the origin. Try a reflection.