The general equation of a circle with center (h, k) and radius, r, is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]If the center is at the origin:
(h, k) = (0, 0)
Substitute h = 0 and k = 0 into the general equation above
[tex]\begin{gathered} (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}[/tex]Therefore, the standard form of the equation of a circle whose center is at the origin is:
[tex]x^2+y^2=r^2[/tex]