Standard Form (Centre at Origin)

Standard Form: Centre at the Origin

Let the centre of the circle be the origin $O(0,0)$ and let the radius be $r$. Let $P(x,y)$ be any point lying on the circle. Because $P$ is on the circle, its distance from the centre must equal the radius:

Applying the distance formula between $O(0,0)$ and $P(x,y)$:

Since $OP=r$, squaring gives $OP^2=r^2$, so

$x^2+y^2=r^2$ …