You know that the center of this ellipse is at this point:
[tex](0,0)[/tex]Therefore, it is centered at the Origin.
The Standard form of the equation of a ellipse centered at the Origin, is:
1. When it is horizontal:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]Where:
[tex]a>b[/tex]2. When it is vertical:
[tex]\frac{x^2}{b^2^{}}+\frac{y^2}{a^2^{}}=1[/tex]Where:
[tex]a>b[/tex]It is important to know that the coordinates of the vertices, when it is horizontal, is given by:
[tex](\pm a,0)[/tex]And the coordinates of the co-vertices are:
[tex](0,\pm b)[/tex]When it is vertical, the vertices are:
[tex](0,\pm a)[/tex]And the co-vertices:
[tex](\pm b,0)[/tex]You know that, in this case, the ellipse is 10 units high and 8 units wide, then you can identify that it is vertical.
Therefore, you can find "a" and "b" as following:
[tex]\begin{gathered} a=\frac{10}{2}=5 \\ \\ b=\frac{8}{2}=4 \end{gathered}[/tex]Then, its equation in Standard form is:
[tex]\begin{gathered} \\ \\ \frac{x^2}{16^{}}+\frac{y^2}{25^{}}=1 \end{gathered}[/tex]The answer is: Second option.
