The major axis of ellipse has end points (8,4) and (-4,4). If the ellipse passes through the origin, what is the equation of the ellipse?

My solution:

End points (8,4) and (-4,4)

so 2a = 12, a =6

therefore:

x²/a² + y²/b² =1

x²/6² + y²/b² =1

Passes through origin, put (0,0) in x and y:

0²/6² + 0²/b² =1

b² = 0

b = 0

So the equation for the ellipse is:

x²/6² + y² =1

Did I do this right? Is it really x²/6² + y² =1 ?

Thanks.