Consider that the standard equation of an ellipse is given by,
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Given that the eliipse has center (h,k) as (0,0), and the length of major axis and minor axis is 16 units and 10 units, respectively,
[tex]\begin{gathered} 2a=16\Rightarrow a=8 \\ 2b=10\Rightarrow b=5 \end{gathered}[/tex]Substitute the values in the equation,
[tex]\begin{gathered} \frac{x^2}{8^2}+\frac{y^2}{5^2}=1 \\ \frac{x^2}{64}+\frac{y^2}{25}=1 \end{gathered}[/tex]Thus, the required equation of ellipse is obtained as,
[tex]\frac{x^2}{64}+\frac{y^2}{25}=1[/tex]