$P(a \sec \theta, b \tan \theta)$ and $Q(a \sec \phi, b \tan \phi)$ are two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ where, $\phi+\theta=\frac{\pi}{2}$. If $(h, k)$ is the point of intersection of the normals drawn at $P$ and $Q$, then $k=$

Let $S$ be the focus of the hyperbola $x^2-2 y^2=1$ lying on the positive $X$-axis. Let $P(-1,1)$ be a given point. Then, the area of the triangle formed by the line $P S$ with the coordinate axes is (in sq. units)

If $P\left(\frac{\pi}{6}\right)$ is a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1, S, S$ are its foci and $S P+S P=2 | S P-S P$|, then $e=$