The information given can be represented in the diagram below.
This shows that the ellipse cuts across both sides of the x axis at -9 and +9 to give 18 units wide and the y axis at -4 and 4 to give 8 units high.
The equation of the ellipse is
[tex]\begin{gathered} \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ \end{gathered}[/tex]
"a" is the distance between the origin and where the ellipse cuts across the x axis.
"b" is the distance between the origin and where the ellipse cuts across the y axis.
Therefore, a=9 and b=4
Hence, the equation of the ellipse gives;
[tex]\begin{gathered} \frac{x^2}{9^2}+\frac{y^2}{4^2}=1 \\ \frac{x^2}{81^{}}+\frac{y^2}{16^{}}=1 \end{gathered}[/tex]
In conclusion, the answer is B
