Your objective function is already convex. This follows because the Hessian matrix 
$$\frac2{y^3}\,\begin{bmatrix}
y^2&-xy\\-xy&x^2
\end{bmatrix}$$
of the map $\mathbb R\times(0,\infty)\ni(x,y)\to y\Big(\dfrac xy-r\Big)^2$ is positive semidefinite, for any given real $r$.