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# Equations of a circle with given center and radius in different forms

This online calculator displays equations of a circle in standard form, in parametric form and in general form given center and radius of a circle

This online calculator displays equations of a circle in standard form, in parametric form and in general form given center $(x_0, y_0)$ and radius $r$ of a circle. Formulas can be found below the calculator.

### Equations of a circle with given centre and radius in different forms

#### Center

Standard equation of a circle

General form of the equation of a circle

Parametric equations of a circle

## Standard Equation of a Circle

The standard equation of a circle with the center at $(x_0, y_0)$ and radius $r$ is
$(x^2-x_0) + (y^2-y_0)=r^2$

## Parametric Equations of a Circle

The parametric equations of a circle with the center at $(x_0, y_0)$ and radius $r$ are
$x=r cos \theta + x_0\\y=r sin \theta + y_0$

## General Equation of a Circle

The general equation of a circle with the center at $(x_0, y_0)$ and radius $r$ is
$x^2+ax+y^2+by+c=0$,
where
$a=-2x_0\\b=-2y_0\\c=x^2_0+y^2_0-r^2$