Q.Find the centre and radius of the circle $x^2+y^2=25$.

A circle is the set of every point in a plane that lies at one fixed distance (the radius $r$) from one fixed point (the centre). When the centre is placed at the origin $O(0,0)$, a general point $P(x,y)$ on the circle satisfies $OP=r$. Squaring this distance-formula statement, $OP^2=x^2+y^2=r^2$, gives the standard equation

$x^2+y^2=r^2$ …