we know that
the equation of the circle in center radius form is equal to
(x-h)^2+(y-k)^2=r^2
where
(h,k) is the center and r is the radius
so
Verify each circle
Part 1
purple circle
The first circle has a radius of 6 units
r=6 units
center (2,-1)
the equation is
(x-2)^2+(y+1)^2=6^2
(x-2)^2+(y+1)^2=36
Part 2
red circle
r=3 units
center (-1,-3)
so
(x+1)^2+(y+3)^2=3^2
(x+1)^2+(y+3)^2=9
Part 3
blue circle
r=3 units
center (1,3)
so
(x-1)^2+(y-3)^2=3^2
(x-1)^2+(y-3)^2=9
Part 4
green circle
r=2 units
center(2,-3)
so
(x-2)^2+(y+3)^2=2^2
(x-2)^2+(y+3)^2=4