Example 2. A chord with slope $t$ is drawn through the endpoint $(-a, 0)$ of the real axis of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$. Find the equation of the line passing through the other endpoint of the chord and the endpoint $(a, 0)$ of the real axis.
According to Theorem 6, the slope $k$ of the required line and $t$ should have the relationship $k \cdot t=\frac{b^{2}}{a^{2}}$, therefore $k=\frac{b^{2}}{a^{2} t}$. Hence, the required line is: $y=\frac{b^{2}}{a^{2} \dot{t}}(x-a)$.