Yes, I much prefer doing this sort of work in After Effects but it is possible to do directly in Final Cut but arguably better & easier within the Motion application of Final Cut Studio.
In FCP, import the media; drop it on the timeline; double click the scene to open it in the Viewer then use the Motion tab to set scale & position keyframes. If this is new to you, expect a learning curve...
Did you say curve? I just finished a 10 sec sequence which has taken hours. Curve more of a steep clif :-)
I asked the question after many attempts to get the file to appear in FC, it did after lots of down sizeing. Then it was ages realising that I had to mark each point with a scale point not just an anchor. It all seams quite simple now but learning which order to do things in took sometime as well.