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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.

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

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

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