Answer
$$e = \frac{1}{9}$$
Work Step by Step
$$\eqalign{
& {\text{From the graph we can see:}} \cr
& {\text{Focus }}\left( { - 4,0} \right){\text{ and the point }}\left( {4,\frac{{10}}{3}} \right),\,\,\,d = 9 \cr
& {\text{The equation of the ellipse is }}\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1 \cr
& {\text{Foci}}\left( { \pm c,0} \right) \to c = 4 \cr
& {\text{The exccentricity is }}e = \frac{c}{a} = \frac{a}{d} \cr
& {a^2} = cd \cr
& {a^2} = \left( 9 \right)\left( 4 \right) \cr
& {a^2} = 36 \cr
& \cr
& e = \frac{c}{a} = \frac{4}{{36}} \cr
& e = \frac{1}{9} \cr} $$
