The vertical cross-section of a custom-built acoustic shell for an outdoor concert stage is being designed. The shell rests on a flat horizontal stage floor. Using a coordinate system where the origin $O$ is at the left-most point of the shell's base and the $x$-axis lies along the stage, the right-most point of the base is $P$. The shape of the cross-section is modelled by the equation

$$x^2+y^2=k\sqrt{x}-10y$$

where $x$ and $y$ are the horizontal and vertical distances from the origin in metres, and $k$ is a constant.