Definition:Virtual Circle
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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
Sources
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {III}$. The Circle: $14$. To find the equation of the circle whose centre is $\tuple {\alpha, \beta}$ and radius $r$