$$\begin{gathered} \mathrm{The} \mathrm{equation} \mathrm{of} \mathrm{the} \mathrm{hyperbola} \mathrm{which} \mathrm{passes} \mathrm{throug} \mathrm{the} \mathrm{point} (2,3) \mathrm{and} \mathrm{has} \mathrm{the} \mathrm{asymptotes} 4\mathrm{x}+3\mathrm{y}-7=0 \mathrm{and} \\ \mathrm{x}-2\mathrm{y}-1=0 \mathrm{is} \end{gathered}$$

$$\begin{gathered} Given equations of asymptotes are 4x+3y-7=0,x-2y-1=0 \\ Now equation of h\mathrm{yperbola} \mathrm{is} (4\mathrm{x}+3\mathrm{y}-7)(\mathrm{x}-2\mathrm{y}-1)+k=0 \\ It passes through the point (2,3) then \\ (8+9-7)(2-6-1)+k=0 \\ \Rightarrow 10(-5)+k=0 \\ \Rightarrow k=50 \\ \therefore Equation of hyperbola is 4x^2-5xy-6y^2-11x+11y+57=0 \end{gathered}$$