The equation of normal to the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ at the point $(a\sec \theta ,b\tan \theta )$ is $$\frac{{ax}}{{\sec \theta }} + \frac{{by}}{{\tan \theta }} = {a^2} + {b^2} = {a^2}{e^2}$$
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