# Thread: Help with writing standard form of ellipse and hyperbola equations

1. ## Help with writing standard form of ellipse and hyperbola equations

Here's the problem I'm stuck on:

Vertices: (17, 1), (-11, 1)
Foci: (3 + 7root3, 1), (3 - 7root3, 1)

If you could also show some work and explain how you did it, that would be great! Thanks in advance!

2. Originally Posted by Rolltide93
Here's the problem I'm stuck on:

Vertices: (17, 1), (-11, 1)
Foci: (3 + 7root3, 1), (3 - 7root3, 1)

If you could also show some work and explain how you did it, that would be great! Thanks in advance!
1. The ellipse you are looking for (axes parallel to the coordinate axes) has the general equation:

$\displaystyle \dfrac{(x-x_M)^2}{a^2}+\dfrac{(y-y_M)^2}{b^2}=1$

where a, b denote the semi-axes of the ellipse and $\displaystyle x_M, y_M$ denote the coordinates of the center of the ellipse.

2. The center is the midpoint of the line segment between the vertices, that means the coordinates of the center are the means of the coordinates of the vertices.

3. The distance between the center and one vertex is a.
The distance between the center and the focus is e which is calculated by:

$\displaystyle e^2=a^2-b^2$

Since you already know a and e determine b.

4. Plug in all values into the general equation of the ellipse.