# Math/Algebra

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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).

• Math/Algebra -

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(25-16)=3

So the equation for the given ellipse is
x²/5²+y²/3²=1

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