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(C) The equation of a hyperbola with asymptotes $L_1=0$ and $L_2=0$ is given by $L_1 \cdot L_2 + k = 0$.Here,the asymptotes are $(4x+3y-7)=0$ and $(x-

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$4x^2-5xy-6y^2-11x+11y+57=0$

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(C) The equation of a hyperbola with asymptotes $L_1=0$ and $L_2=0$ is given by $L_1 \cdot L_2 + k = 0$.Here,the asymptotes are $(4x+3y-7)=0$ and $(x-2y-1)=0$.So,the equation of the hyperbola is $(4x+3y-7)(x-2y-1)+k=0$ ...$(i)$Since the hyperbola passes through the point $(2,3)$,we substitute $x=2$ and $y=3$ into Eq. $(i)$:$(4(2)+3(3)-7)(2-2(3)-1)+k=0$$(8+9-7)(2-6-1)+k=0$$(10)(-5)+k=0$$-50+k=0 \Rightarrow k=50$Substituting $k=50$ into Eq. $(i)$:$(4x+3y-7)(x-2y-1)+50=0$$4x^2-8xy-4x+3xy-6y^2-3y-7x+14y+7+50=0$$4x^2-5xy-6y^2-11x+11y+57=0$

The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is

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