lets assume I have equation like X^2+Y^2+Z^2=M^2 and didn't say anything about it, so it's in general.

afterwards we have conclude over specific case that case is satisfying the equation over specific parameter like Z=0 , then can I say that "specific case" is satisfying that equation: X^2+Y^2=M^2 ?! if so then why? I'm stuck in that struggle everyday, how we can assign specific parameter over specific case and then we say it's satisfying the general equation over specific parameter ! ?!