Let an ellipse \(\frac{{x}^{2}}{9}+\frac{{y}^{2}}{4}=1\). If Mid point of Chord is \(\left(\sqrt{2},\frac{4}{3}\right)\)…

Let an ellipse \(\frac{{x}^{2}}{9}+\frac{{y}^{2}}{4}=1\). If Mid point of Chord is \(\left(\sqrt{2},\frac{4}{3}\right)\). If length of this Chord is \(\frac{2\sqrt{\alpha }}{3}\) .Find value of \(\alpha\).