Doubts about the meaning of "canonical"

Hi there. I have a doubt about what we are talking about when we ask, in linear algebra, for the canonical form of a conic.

The doubt is basically, if for example, the canonical form of a circle includes a circle translated at any point, for example:

Or if it only reefers to the circle when it is centered at the origin, and then if I have that equation I must make a translation to get:

Essentially its the same, but I'm not sure when it is in the canonical form, and what the canonical forms of a conic are, and what isn't.

Thats all.

Thanks for posting and over :P