Find the parametric form of the equation of the circle `x^2+y^2+p x+p y=0.`

Explanation

The equation of the circle can be rewritten in the form
`(x+(P)/(2))^(2)+(y+(p)/(2))^(2)=(p^(2))/(2)`
Therefore, the parametric form of the equation of the given circle is
`x=-(p)/(2)+(p)/(sqrt(2))cos theta`
`=(p)/(2)(-1+sqrt(2)cos theta)`
and `y= -(p)/(2)+(p)/(sqrt(2)) sin theta`
`=(p)/(2)(-1+sqrt(2)sin theta)`
where `0 lethetalt2pi`