Math/Algebra
posted by M .
Find the standard equation of an ellipse with the given characteristics and sketch the graph.
Vertices at (0,5), and (0,5); Foci at (0,4)and (0,4).

The ellipse is centred at the origin (0,0).
The standard formula for the ellipse is then
x²/a²+y²/b²=1
where
2a=distance between vertices on the major axis
=(5(5)=10, so
a=5
Distance between foci
2c=(4(4))=8
so
c=4
To find b, we use the relation
a²=b²+c²
or
5²=b²+4²
b=sqrt(2516)=3
So the equation for the given ellipse is
x²/5²+y²/3²=1