Example + Find the equation of the hyperbola passing through the point $(-1,3)$ and having the same asymptotes as the hyperbola $\frac{x^{2}}{4}-\frac{y^{2}}{9}=1$.
Solution: The equation of the hyperbola can be set as $\frac{x^{2}}{4}-\frac{y^{2}}{9}=\lambda$. Substituting $(-1,3)$, we get $\lambda=-\frac{3}{4}$. Therefore, the equation of the hyperbola is $-\frac{x^{2}}{3}+\frac{4 y^{2}}{27}=1$.

Comment: The family of hyperbolas that share the same asymptotes with the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=\lambda$.