Finding equation of an Ellipse

[koriemo]

I have to find the equation of the ellpse with foci (-7,-12) and (-7,18) and a major axis that is 34 units long.

I already found that the vertices are at (-7,20) and (-7,-14) and the center is at (-7,3)

But I don't know how to find the co-vertices to get the equation.

Thanks so much!

 

[tkhunny]

\(\displaystyle \L\;c^{2}\;=\;a^{2}\;-\;b^{2}\)?

 

[koriemo]

\(\displaystyle \L\;c^{2}\;=\;a^{2}\;-\;b^{2}\)?

I tried that, but I don't know a or b...

 

[skeeter]

your major axis runs in the y-direction ... so c² = b² - a²

in this case, isn't b = 1/2 the major axis = 17?

and c = 15, correct?

looks like a = 8

co-vertices at (1,3) and (-15,3), no?

equation would be ...

(x+7)²/8² + (y-3)²/17² = 1

 

[stapel]

\(\displaystyle \L\;c^{2}\;=\;a^{2}\;-\;b^{2}\)?

I tried that, but I don't know a or b...

You are given information that tells you that the ellipse has an equation of the form:

. . . . .(x - h)² / b² + (y - k)² / a² = 1

...where (h, k) is the center, 2a is the length of the major axis, 2b is the length of the minor axis, and the foci are (h, k - c) and (h, k + c), where c relates to a and b by the formula provided earlier.

Since you are given the foci and the major-axis length, you should be able to determine c, and then b. This will give you the co-vertices.

Eliz.