Understanding focal length (Camera intrinsics)

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I'd like to know if my understanding is correct regarding camera focal length.

The intrinsics of the camera consists the focal length (and of course other parameters, not focusing on them here..) which is really derived from the two parameters Fx and Fy, where in cameras that provide us square images the parameters of the focal length hold the following attribute: Fx=Fy=F (for my understanding, not 100% sure regarding this), unlike rectangular images case, where Fx and Fy differ.

Is it correct that this occurs from the fact that the width and height of an object will be reduced in different proportions according to the distance between the object and the camera?

If my claim does hold, than if i am to calibrate a camera where the image i'm receiving has very big width/height ratio, than i should anticipate that Fx and Fy will differ largely?

Thanks in advance.