Question Number 150331 by ajfour last updated on 11/Aug/21
$${ultimately}\:\:{Q}.\mathrm{149894}\:\:{boils}\: \\ $$$${down}\:{to}\:{finding}\:{s}_{{max}} ,\:{s}_{{min}} \:\forall \\ $$$$\:\:\:\:\left\{{h}−{s}\mathrm{cos}\:\left(\theta−\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} \\ $$$$+\left\{{k}−{s}\mathrm{sin}\:\left(\theta+\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$ \\ $$