Posted by **M** on Sunday, May 26, 2013 at 3:22am.

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 -
**MathMate**, Sunday, May 26, 2013 at 10:22am
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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