If the eccentricity of a hyperbola $\frac{x^2}{9} - \frac{y^2}{b^2} = 1,$ which passes through $(K, 2),$ is $\frac{\sqrt{13}}{3},$ then the value of $K^2$ is

What is the area of the triangle formed by the lines $x - y = 0$,$x + y = 0$,and any tangent to the hyperbola $x^{2} - y^{2} = a^{2}$?

The vertices of a hyperbola are at $(0, 0)$ and $(10, 0)$ and one of its foci is at $(18, 0)$. The equation of the hyperbola is:

Find the coordinates of the foci and the vertices,the eccentricity,and the length of the latus rectum of the hyperbola $5y^{2} - 9x^{2} = 36$.

The asymptotes of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ form with any tangent to the hyperbola a triangle whose area is $a^2 \tan \lambda$ in magnitude. Then its eccentricity $e$ is:

If $3x + 2\sqrt{2}y + k = 0$ is a normal to the hyperbola $4x^2 - 9y^2 - 36 = 0$ making positive intercepts on both the axes,then $k=$ (in $\sqrt{2}$)