Hardness of EC-based DLP

Question

I have a question about EC-based DLP. I know that getting $k$ is hard when $kG$ is known. ($G$ is a generator)

Question:

Is it still hard getting $kG$ where $x$ is known? (in here, $kG=(x,y)$) or getting $k$ where $x$ is known?

I think the former is not computationally hard. Am I right?

Answer 1

For a given x there are only two possible y coordinates figuring that out is just a matter of solving the curve equation for y.

Afterwards you just end up with a regular DLOG problem which is hard (if your x is for a point with large enough order order your curve order is prime).