Answer:
[tex]\frac{x^2}{144}+\frac{y^2}{80}=1[/tex]
Step-by-step explanation:
We want to find the equation of an ellipse with foci at (8,0) and (-8,0) and a vertex at (12,0)
This is a horizontal ellipse with its center at the origin.
The equation is of the form:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Since the vertex is at (0,12)------>a=12
Since the foci is at [tex](\pm8,0)[/tex], we have c=8
Using [tex]a^2-b^2=c^2[/tex]
We have [tex]12^2-b^2=8^2[/tex]
[tex]b^2=12^2-8^2[/tex]
[tex]b^2=80[/tex]
Our equation now becomes:
[tex]\frac{x^2}{12^2}+\frac{y^2}{80}=1[/tex]
Or
[tex]\frac{x^2}{144}+\frac{y^2}{80}=1[/tex]
