Creating Path

[sharp osprey]

I am definitely lost on what you are trying to do.
how is this path related to your eclipse? are you trying to generate an ecliptic path? if so, that should be trivial, just substitute x or y in the equation of eclipse to get the other value.
is the path varying in two dimensions only? (like in i, j directions ? even if it is in 3D space)

regarding shortening your x to compensate for y, I am still not sure what you are trying to do (the whole picture), so I would appreciate an example, never the less,
if want to know how much, then I assume you are talking about a fixed length, which immediately brings the famous theorm
c^2 = a^2 + b^2
as you increase y, as long as it is not exceeding c^2 (becomes 90 degree right angle) then you can easily get x by
sqrt(c^2 - y^2)
of course, you had have calculate c^2 first, which I assume in your case is the distance between two points on your path

Creating Path

[velvet island]

I found that the solution was the easiest one, rotate the empty game object that I am orbiting.

[sharp osprey]

pure rotation, will not give you ecliptic path
it will give you circular paths

but yeah if u want to rotate around 2 axes,
namely i and j,
Then just dot product with them shall give your coordinate with respect to them

[velvet island]

I'm using local position to move the object that is orbiting.
it's difficult to show due to perspective but it seems to work, thanks for the input :D

[sharp osprey]

yeah, but again, this is circular path and not ecliptic

[velvet island]

I can make it elliptical