Application Of Derivatives

If the straight line \(x \cos \alpha+y \sin \alpha=p\) touches the curve \(\left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2\) at the point \((a, b)\) on it and \(\frac{1}{a^2}+\frac{1}{b^2}=\frac{k}{p^2}\), then \(k=\)