Answer:
[tex]\frac{x^2}{25}+\frac{y^2}{64}=1[/tex]
Step-by-step explanation:
If the ellipse has a vertical major axis of length 16, then
[tex]2a=16[/tex]
[tex]\Rightarrow a=8[/tex]
If the ellipse has the length of the minor axis to be 10, then;
[tex]2b=10[/tex]
[tex]\Rightarrow b=5[/tex]
The equation of the ellipse is given by;
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]
Thus;
[tex]\frac{x^2}{5^2}+\frac{y^2}{8^2}=1[/tex]
[tex]\frac{x^2}{25}+\frac{y^2}{64}=1[/tex]
