Definition:Virtual Circle

Definition
A virtual circle is the locus in the Cartesian plane of an equation of the form:


 * $(1): \quad \paren {x - a}^2 + \paren {y - b}^2 + r^2 = 0$

where $a$, $b$ and $r$ are real constants.

There are no solutions to $(1)$ in real numbers, and so the locus of $(1)$ consists entirely of imaginary points.

Also see

 * Definition:Point-Circle


 * Characteristic of Quadratic Equation that Represents Circle‎