Definition:Point-Circle

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


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

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

There is only one point in the Cartesian plane which satisfies $(1)$, and that is the point $\tuple {a, b}$.

It can be considered to be a circle whose radius is equal to zero.

Also known as
A point-circle is also known as a degenerate circle.

Also see

 * Definition:Virtual Circle


 * Characteristic of Quadratic Equation that Represents Circle‎