Why is a circle 1-dimensional?

Question

In the textbook I am reading, it says a dimension is the number of independent parameters needed to specify a point. In order to make a circle, you need two points to specify the $x$ and $y$ position of a circle, but apparently a circle can be described with only the $x$-coordinate? How is this possible without the $y$-coordinate also?

Answer 1

You conflate drawing a circle on the 0xy plane and the definition of a circle.

The definition of a circle is the locus of points (no dimension) equidistant from another point (also no dimension). These points create a line. And that is one-dimensional.