Find standard form of the ellipse with a center of: (2,-1), and a vertex of:(2,8)

I think that the minor axis of length is 5, but I'm not positive.

I know that the formula is

(X-h)^2/a^2 + (y-k)^2/b^2 = 1

Question

Find standard form of the ellipse with a center of: (2,-1), and a vertex of:(2,8)

I think that the minor axis of length is 5, but I'm not positive.

I know that the formula is

(X-h)^2/a^2 + (y-k)^2/b^2 = 1

mertsj · Answer

a = 9, a^2=81
If b = 5, b^2 = 25
This ellipse has major axis vertical so a^2 is under y^2

mertsj · Answer

$$\frac{(x-2)^2}{25}+\frac{(y+1)^2}{81}=1$$

mertsj · Answer

I don't know how you got that b = 5 but if it does, that is the equation.

anonymous · Answer

What would you do if it didn't equal five?

mertsj · Answer

You would have to have more information.

anonymous · Answer

Alright then, thank you so much for your help!

mertsj · Answer

Actually, if the length of the minor axis is 5 then b = 5/2 and b^2=25/4

mertsj · Answer

yw

mertsj · Answer

Does the problem give any additional information?  Perhaps something about the foci or something?

anonymous · Answer

No. But I think that the minor axis of length is 5.

mertsj · Answer

Why do you think that?

mertsj · Answer

If you have posted the entire problem, there is nothing to suggest that.

anonymous · Answer

Because I copied down the problem from memory and that was part of the additional information.

anonymous · Answer

But I'm not positive.

mertsj · Answer

ok.  Then 5 = 5/2

mertsj · Answer

Or maybe it gave the distance from the center to the co-vertex.

mertsj · Answer

Anyway, if you understand how to do the problem, the number isn't so important.

anonymous · Answer

Alright, I think I'm getting it. Thanks for your help!