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

If the equation of the tangent drawn at $(h, k)$ to the hyperbola $\frac{(x-1)^2}{1}-\frac{(y-2)^2}{2}=1$ is $x=2$,then $h+k=$

If the eccentricity of the hyperbola $\frac{x^2}{9} - \frac{y^2}{b^2} = 1$ passing through the point $(k, 2)$ is $\frac{\sqrt{13}}{3}$,then the value of $k^2$ is:

If $e_1$ and $e_2$ are respectively the eccentricities of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and its conjugate hyperbola,then the line $\frac{x}{2 e_1}+\frac{y}{2 e_2}=1$ touches the circle having centre at the origin. Find its radius.

If the eccentricity of a hyperbola is $\sqrt{3}$,then the eccentricity of its conjugate hyperbola is:

The locus of a variable point whose chord of contact with respect to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ subtends a right angle at the origin is