First note that the area of this circle would be
If we place the circle on a set of axes centred at the origin, it has equation then draw in the vertical line somewhere to the right of the y-axis, we wish to know what value of x this is so that it splits the circle into areas in the ratio 2:1. So that means the area bounded between this line and the circle on the right will be , and since this is evenly distributed above and below the x-axis, the area above the x-axis is .
So we can set up an integral for the area bounded by the circle, the x-axis and the vertical line as .
Equating this to the known area we have .
In order to evaluate this integral and solve for the value of a, we need to make a trigonometric substitution and note that when and when . Substituting gives
Unfortunately there is no way to evaluate the value of a here exactly, but you should be able to get a numerical answer using a CAS