$\text{The equation of a rectangular hyperbola whose asymptotes}$$\text{ are }x=3\text{ and }y=5\text{ and passing through }(7,8)\text{ is }$

$\text{The equation of the rectangular hyperbola is}(x-3)(y-5)+\lambda =0$

$\text{ It passes through }(7,8)\text{ . Hence, }$

$\begin{array}{l}4\times 3+\lambda \text{ or }\lambda =-12\\ \therefore xy-5x-3y+15-12=0\\ \text{ or }xy-3y-5x+3=0\end{array}$