The radius of the director circle of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is

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

The eccentricity of the curve $x^2 - y^2 = 1$ is

If the area of the quadrilateral formed by the tangents drawn at the ends of the latus rectum of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is equal to the square of the distance between the center and one focus of the hyperbola,then $e^3$ is ($e$ is the eccentricity of the hyperbola).

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

If the variable line $y = kx + 2h$ is tangent to an ellipse $2x^2 + 3y^2 = 6$,the locus of $P(h, k)$ is a conic $C$ whose eccentricity equals