I don't get what to do at all...
Find the curve such that the tangent line at any of its points P bisects the angle between the ordinate at P and the line joining P and the origin.
The word "tangent" of the curve means $\displaystyle dy/dx$ where $\displaystyle y(x)$ is the function describing the curve. I think the question is telling you that this tangent line pass through the origin to the point q=(0.5x,y) for any point P=(x,y).