If $\frac{x^{2}}{36}-\frac{y^{2}}{k^{2}}=1$ is a hyperbola,then which of the following statements can be true?

Let the domain of the function $f(x) = \log_{3}\log_{5}\log_{7}(9x - x^{2} - 13)$ be the interval $(m, n)$. Let the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ have eccentricity $\frac{n}{3}$ and the length of the latus rectum $\frac{8m}{3}$. Then $b^{2} - a^{2}$ is equal to:

For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,if the length of the transverse axis is $8$ and the distance between the foci is $2\sqrt{41}$,then the length of its latus rectum is

The normal to the rectangular hyperbola $xy = c^{2}$ at the point $t$ meets the curve again at a point $t'$,such that

The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is $16$ and eccentricity is $\sqrt{2}$ is:

The equation of the transverse axis of the hyperbola $(x-3)^2+(y+1)^2=(4x+3y)^2$ is