Answer:
[tex]\frac{x^2}{20}+\frac{y^2}{36}=1[/tex]
Step-by-step explanation:
We want to find the equation of an ellipse with foci at (0,4) and (0,-4), and vertices at (0,6), (0,-6).
Since the major axis is on the y-axis the equation of this ellipse which is centered at the origin is given by:
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]
Using [tex]b^2=a^2-c^2[/tex] we obtain:
[tex]b^2=6^2-4^2[/tex]
[tex]b^2=36-16[/tex]
[tex]b^2=20[/tex]
Hence the required equation is [tex]\frac{x^2}{20}+\frac{y^2}{36}=1[/tex]
