6. The hyperbola with asymptotes $2 x \pm 3 y=0$ and passing through the point $(1,2)$ is

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6. $\frac{9}{32} y^{2}-\frac{x^{2}}{8}=1$ can be set as the equation $4 x^{2}-9 y^{2}=\lambda$, substituting $(1,2)$, we can find $\lambda$.
