Respuesta :
Given:
The vertices of the ellipse are at (0,6) and (0,-6) and co-vertices at (4,0) and (-4,0).
Required:
We have to find the equation of the ellipse.
Explanation:
The vertices are at (0,6) and (0,-6) then the length of the major axis is 6.
The co-vertices are at (4,0) and (-4,0) then the length of the minor axis is 4.
We know that the standard form of an ellipse is
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]Where a and b are the length of the major axis and the minor axis respectively.
Then the required equation of the ellipse is
[tex]\begin{gathered} \frac{x^2}{6^2}+\frac{y^2}{4^2}=1 \\ \\ \Rightarrow\frac{x^2}{36}+\frac{y^2}{16}=1 \end{gathered}[/tex]Final answer:
Hence the final answer is
[tex]\frac{x^2}{36}+\frac{y^2}{16}=1[/tex]