The tangent at an extremely (in the first quadrant) of latus rectum of the hyperbola $\;\large\frac{x^{2}}{4}-\large\frac{y^{2}}{5}=0\;$ , meets x -axis and y -axis at A and B respectively .Then $\;(OA)^{2}-(OB)^{2}\;$ , where O is the origin , equals :

Question

$(a)\;-\large\frac{20}{9} \qquad(b)\;-\large\frac{16}{9} \qquad(c)\;-4\qquad(d)\;-\large\frac{4}{3}$