Quadritic curves, how can foci = vertice?

[flyingpig]

Homework Statement

[PLAIN]http://img688.imageshack.us/img688/5336/unledaty.jpg

The Attempt at a Solution

I underlined a = 3, which doesn't make sense seeing the foci is at (plus/minus3, 3)

How can this be?? Wouldn't that make a straight line?

 

[eumyang]

You're confusing distances and points.

a is the distance between the center and a vertex. The vertices are where the blue curve intersects the focal axis. This distance a = 3.

I use the letter c to indicate the distance between the center and a focus. You can see that while one of the foci is (3, 3), the distance c between the center (which is (0, 0)) and this focus is
3\sqrt{2}
, not 3.

 

[flyingpig]

Oh right okay thanks lol