I'm stumped on how to formalize these two sentences properly into predicate logic.

1: There's a city to which all roads lead.

2: All roads lead to a city.

The question says nothing about defining a Universe of Discourse.

I tried using

R = is a road

C = is a city

L = leads to

1: If there exists a city and then every road leads to this city.

(∀y)(∃x)[(Cx & Ry) -> Lyx)]

I'm unsure about my use of the existential quantifier, it seems to me that what I wrote translates more into "If there exists a city and each road then each road leads to this city." I'm very confused at this point because this doesn't seem to make sense to me at all.

2: Everything that is a road leads to a city.

(∀y)(Ry -> Lyx)

With this one I started writing it and I know that x is unqualified and unquantified because I realized that if I were to add something like (∃x)(Cx) then this one would be identical to the first question. Is that right? I'm sure it is not since the first one says that "All roads lead to a specific city" whereas the second question says that "All roads lead to at least one city".