The locus of the midpoints of the parallel chords with gradient $m$ of the rectangular hyperbola $xy = c^2$ is

The area of the triangle formed by the tangent to the hyperbola $xy = a^2$ and the coordinate axes is:

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

The locus of the point of intersection of the tangents drawn at the extremities of a normal chord of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is

Area of the triangle formed by the lines $x - y = 0$,$x + y = 0$ and any tangent to the hyperbola $x^2 - y^2 = a^2$ is:

The locus of a point whose difference of distance from points $(3, 0)$ and $(-3, 0)$ is $4$,is