The locus of the point of intersection of the straight lines, $tx-2y-3t=0$ and $x-2ty+3=0 \left(t\in R\right),$ is:

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