help with ellipse question

[dumbdad]

Hello, I am trying to help my daughter with her algebra homework. I've never been very good at math and don't remember much of it at all. Been almost 20 years or so since my last math class. I have arranged for tutoring for my daughter, but the first lesson isn't until after this particular assignment is due. Anyhow here is the problem we are having trouble with.


Find the standard form of the equation of the ellipse satisfying the given conditions.
Foci: (-2, 0), (2,0)
vertices: (-8,0), (8,0)

Any help you can give us would be great!!

 

[galactus]

We'll try to help then.

Since the foci are on the x-axis and are the same distance from the origin, the

major axis is on the x-axis and the ellipse has center (0,0). Thus, a general

equation of an ellipse is: \(\displaystyle \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)

Since the vertices are \(\displaystyle ({\pm}8,0)\), we can say a=8. Since the foci are \(\displaystyle ({\pm}{2,0})\), we have c=2. Therefore,

\(\displaystyle b^{2}=a^{2}-c^{2}=64-4=60\)

An equation of the ellipse is:

\(\displaystyle \frac{x^{2}}{64}+\frac{y^{2}}{60}=1\)