I am currently evaluating the WolframAlpha Notebook edition.
It seems as if a request of:
Eliminate[{x == t + 2*((a*t)/Sqrt[1 + 4*t^2]), y == t^2 - a/Sqrt[1 + 4*t^2]}, t]
is not getting answered by WolframAlpha Notebook on a 12th Intel-i7 8-Core PC with 32GB Ram. This is a bit dissapointing, we have much more complex problems in future to be solved by Wolfram.
Do I make a mistake ?