Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^2−18e+5=0$. If $S(5, 0)$ is a focus and $5x=9$ is the corresponding directrix of this hyperbola, then $a^2−b^2$ is equal to

Question

$\begin{array}{1 1} (1) 7 \\ (2) -7 \\ (3) 5\\ (4) -5 \end{array}$