Answer
$$\frac{{{x^2}}}{{100}} + \frac{{{y^2}}}{{64}} = 1$$
Work Step by Step
$$\eqalign{
& {\text{From the graph we can see that the orientation of Major Axis is}} \cr
& {\text{Horizontal }}\left( {{\text{along the x - axis}}} \right){\text{ and the ellipse is centered at the }} \cr
& {\text{Origin}}.{\text{ Then}}{\text{, the equation is of the form}} \cr
& \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1 \cr
& \cr
& {\text{The length of the major axis is 20}} \cr
& {\text{2}}a = 20,\,\,\,\,a = 10 \cr
& {\text{The length of the minor axis is 16}} \cr
& 2b = 16,\,\,\,b = 8 \cr
& \cr
& \frac{{{x^2}}}{{{{\left( {10} \right)}^2}}} + \frac{{{y^2}}}{{{{\left( 8 \right)}^2}}} = 1 \cr
& \frac{{{x^2}}}{{100}} + \frac{{{y^2}}}{{64}} = 1 \cr} $$
