If $3 \sqrt{2} x-4 y=12$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{5}{4}$ is its eccentricity, then $a^2-b^2=$

If the normal drawn to the hyperbola $x y=16$ at $(8,2)$ meets the hyperbola again at a point $(\alpha, \beta)$, then $|\beta|+\frac{1}{|\alpha|}=$

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

If a hyperbola has asymptotes $3 x-4 y-1=0$ and $4 x-3 y-6=0$, then the transverse and conjugate axes of that hyperbola are