Since when does 0/b^2 = 1 imply b = 0 and at what point does 1/0 = 1?

Let's try this again...

Yes, a = 6.

But the equation for the ellipse would be:

(x - h)^2/36 + (y - k)^2/b^2 = 1

Now, we know the center of the ellipse is the point (2, 4) since this is the midpoint of the line segment containing the two vertices. Thus h = 2 and k = 4:

(x - 2)^2/36 + (y - 4)^2/b^2 = 1

Now put in the origin:

4/36 + 16/b^2 = 1

1/9 + 16/b^2 = 1

(1/9)b^2 + 16 = b^2

(1/9 - 1)b^2 = -16

-(8/9)b^2 = -16

b^2 = 18

b = sqrt{18}

So:

(x - 2)^2/36 + (y - 4)^2/18 = 1

-Dan