A variable tangent to the hyperbola $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ meets the transverse axis and the tangent at the vertex $\left(\mathrm{a},\mathrm{ }0\right)$ at $\mathrm{Q}$ and $\mathrm{R}$ . If the locus of mid point of $\mathrm{Q}\mathrm{R}$ is $\mathcal{l}\mathrm{x}\mathrm{ }\left({\mathrm{k}\mathrm{y}}^2+{\mathrm{m}\mathrm{b}}^2\right)={\mathrm{a}\mathrm{b}}^2$ then value of ${\mathrm{k}}^2-{\left(\mathcal{l}+\mathrm{m}\right)}^2\mathrm{ }$ is equal to -

The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola $\frac{x^2}{4}-\frac{y^2}{5}=1$, meets the $x$-axis and $y$-axis at $A$ and $B$, respectively. Then $O{A}^2-O{B}^2$, where $O$ is the origin, equals