Question

Find the parametric form of the equation of the circle $x^2+y^2+px+py=0$

Answer 1

$\Rightarrow (x+\frac{p}{2}{)}^2+(y+\frac{p}{2}{)}^2=\frac{p^2}{4}+\frac{p^2}{4}=\frac{p^2}{2}.\therefore Centreis(\frac{-p}{2},\frac{-p}{2})Radius=\frac{p}{\sqrt{2}}.Parameters:\Rightarrow x-\left(\frac{-p}{2}\right)=\frac{p}{\sqrt{2}}\cos \theta \Rightarrow x=\frac{p}{\sqrt{2}}\cos \theta -\frac{p}{2}.(y-(\frac{-p}{2}\left)\right)=\frac{p}{\sqrt{2}}\sin \theta \Rightarrow y=\frac{p}{\sqrt{2}}\sin \theta -\frac{p}{2}\therefore Parameters\to (\frac{p}{\sqrt{2}}\cos \theta -\frac{p}{2},\frac{p}{\sqrt{2}}\sin \theta -\frac{p}{2}).$