# Parametric Equation of Circle

## 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.

(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 + $$\sqrt{g^2 + f^2 – c}$$ $$sin \theta$$