Why is it wrong to conclude a isn't the vertice (conics)

[flyingpig]

Homework Statement

Given the ellipse is centered at the origin and the information, find an equation of the ellipse.

1) An ellipse with focus (\sqrt{5},0), directrix; x = \frac{9}{\sqrt{5}}

2) An ellipse with an eccentricity of 4/5

The Attempt at a Solution

I have to leave right now so I can't post a usuall good attept, but basically for #1) you cannot match the directrix with the a/e, but for #2) you are supposed to take the focus = 4

 

[eumyang]

but for #2) you are supposed to take the focus = 4

Hate to be picky, but a focus is a point, not a number. If
e = c/a,
where c is the distance from the center to a focus, and a is the distance from the center to a vertex (not vertice!), then you should know what a is. All it remains is for you to find b, the distance from the center to an endpoint of the minor axis, and you're done.

 

[HallsofIvy]

Hate to be picky, but a focus is a point, not a number. If
e = c/a,

Yes, flyingpig knows that. He intended \left(\sqrt{5}, 0\right) but, for some reason had only the squareroot in LaTeX and on a separate line.

where c is the distance from the center to a focus, and a is the distance from the center to a vertex (not vertice!), then you should know what a is. All it remains is for you to find b, the distance from the center to an endpoint of the minor axis, and you're done.

Good!

 

[eumyang]

Yes, flyingpig knows that. He intended \left(\sqrt{5}, 0\right) but, for some reason had only the squareroot in LaTeX and on a separate line.

Actually, I was referring to #2, where he writes:

I have to leave right now so I can't post a usuall good attept, but basically for #1) you cannot match the directrix with the a/e, but for #2) you are supposed to take the focus = 4 (emphasis mine)