1) The question makes no sense. If a = b, all the Normals, extended both directions, CONTAIN the center.
2) Okay, I guess it is sufficiently clear that a and b are not equal. I still don't like it.
3) Can you build the Normals?
You'll need a few tools.
1) Find the general derivative of all points on the ellipse.
2) Write the general equation of the tangent line of all points on the ellipse.
3) If you can do #2, you really should be able to write the general equation of all Normals.
4) Calculate the distance of a line from the Origin.
Where shall we start?
Note: The derivative is WAY easier using an implicit method, rather than first solving for y.