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Prove that the product of the lengths of the perpendiculars drawn from the points \( \left(\sqrt{a^{2}-b^{2}}, 0\right) \) and \( \left(-\sqrt{a^{2}-b^{2}}, 0\right) \) to the line \( \frac{x}{a} \cos \theta+\frac{y}{b} \sin \theta=1 \) is \( b^{2} \).
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