R=2; (h, k)=(0,0) standard form of the equation and the general form of the equation of each circle of radius r and canter (h, k)

Standard form of a circle is: (x - h)² + (y - k)² = r² ; where (h,k) is the vertex and r is the radius.

for this example: h = 0, k = 0, and r = 2

(x - 0)² + (y - 0)² = 2² → x² + y² = 4

General form of ANY equation is when everything is one side and 0 is on the other. So, subtract 4 from both sides to get the general equation.

x² + y² - 4 = 0

x² + y² = 4 (standard form) , x² + y² - 4 = 0 (general form)