I think I'm probably making more steps than necessary, but:
The line is perpendicular with the radius (as tangent) therefore there is a rectangular triangle with (0,0), (2,1) and the tangency point (a,b).
We know the length of the hypotenuse (sqrt (5) ) and one of the legs (2-radius). Therefore the distance of this point to (0,0) is 1 and the distance to (2,1). is 2.
1 = sqrt( (a-2)^2 + (b-1)^2)
2 = sqrt( (a-0)^2 + (b-0)^2)
Now it's easy, two equations and two variables. (note that we know a is positive and b is negative as the point has to be in the lower right quadrant).
a=0.8 and b=-0.6
And the following equation for the line that goes through this point and (0,0) is:
y = -0.75*x