Question

what the equation for a circle

Answer 1

if the center is \((h,k)\) and the radius is \(r\) the equation is
\[(x-h)^2+(y-k)^2=r^2\] for example if the center is \((1,-2)\) and the radius is 4, then it will be
\[(x-1)^2+(y+2)^2=16\]

Answer 2

Also if the circle is centred at the origin of the coordinate system, then (h,k) is zero! Thus the equation becomes \[x^{2}+y^{2}=r^{2}\] Look out for these two cases!