The equation of a circle with its center at the origin is `x^2 + y^2 =r^2` where r = radius.
The standard form of the equation of a circle with its center not at the origin is `(x-h)^2 + (y-k)^2 =r^2`
The horizontal (h) and vertical (k) translations indicate the center of the circle. This formula comes from the distance formula where the distance between the center and every point on the circle equals the radius.
In the problem above, the center of the circle is given as (0,0) or the origin with a radius of 2 so we know the equation will be
Let's fill it into the standard form of the equation.
`(x+0)^2 + (y+0)^2 =r^2`
`(x+0)^2 + (y+0)^2 = 2^2`
`(x+0)^2 + (y+0)^2 =4`
Remove the 0 from the polynomial since adding or subtracting 0 will not change the value of the expression.
`x^2 +y^2 =4`
The equation of the circle with its center at (0,0) and radius 2 is x^2 +y^2 =4.