Why does the elliptical wing planform have two different types of curves?
It's because the center axis for the ellipses has to be along the thickest section of the wing, because there is also a taper in thickness that must be accommodated as the ribs get smaller and smaller toward the tip.  In your sketch, the thickest section is at 40% of chord and the taper in both planform and thickness must be oriented to that 40% chord line, hence the asymmetrical curves.
The placement of the axis of maximum thickness is a function of the particular airfoil selected, that is, the point of maximum thickness of the airfoil section itself.  For structural efficiency, this is normally also the location for the main spar. In the sketch, which resembles a Spitfire wing planform, the broken line will be more or less the main spar location, with the nose ribs on the left and the main ribs on the right, with the ellipse curves placed to maintain the 40% forward/60% aft ratio out to the tip.
If the thickest section of the wing was at 50% of chord, then the ellipses would be symmetrical.