Unknown number called me on FaceTime and activated my camera. How to prevent?

That person didn't activate your camera. FaceTime activated it in anticipation of you answering the FaceTime call. Just don't accept calls, especially FaceTime, of numbers you don't know. Your camera did not send anything back to that person unless you actually answered the call.

asa1968 wrote:

But FT did not turn off the camera until I closed FT. I did not accept the call. It simply 'arrived' and I took note but I did not 'answer' it. Thanks for your help.

That’s how FaceTime works. When you open it, the camera is enabled. It doesn’t matter if you are actually engaged in a call.

You can block that caller in the FaceTime preferences, change how you can be reached on the FaceTime preference panel, disable calls from iPhone, if that was the source, or you can disconnect the external camera (or duct tape the internal camera) to prevent video access to you.

I had this problem once, and just disconnected by external camera and blocked the miscreant that had initiated the FaceTime call.