Parametric Equation of Circle
(i) The parametric equation of circle \(x^2 + y^2\) = \(r^2\) are
x = rcos\(\theta\), y = rsin\(\theta\) ; \(\theta\) \(\in\) [0,2\(\pi\))
and (rcos\(\theta\), rsin\(\theta\)) are called parametric coordinates.
Also Read : General Equation of the Circle – Formula and Examples
(ii) The parametric equation of circle \((x – h)^2 + (y – k)^2\) = \(r^2\) are
x = h + rcos\(\theta\), y = k + rsin\(\theta\)
where \(\theta\) is parameter.
(iii) The parametric equation of the circle \(x^2 + y^2 +2gx + 2fy + c\) = 0
x = – g + \(\sqrt{g^2 + f^2 – c}\) \(cos \theta\)
y = -f + \(\sqrt{g^2 + f^2 – c}\) \(sin \theta\)
