Eccentricity of rectangular hyperbola is

Let $\mathrm{P}$ be a point on the hyperbola $\mathrm{H}: \frac{\mathrm{x}^2}{9}-\frac{\mathrm{y}^2}{4}=1$, in the first quadrant such that the area of triangle formed by $\mathrm{P}$ and the two foci of $\mathrm{H}$ is $2 \sqrt{13}$. Then, the square of the distance of $\mathrm{P}$ from the origin is

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

The equation of the hyperbola whose conjugate axis is $5$ and the distance between the foci is $13$, is

The equation of the tangent parallel to $y – x + 5 = 0$ drawn to $\frac{{{x^2}}}{3} – \frac{{{y^2}}}{2} = 1$ is