The stand form of the circle is
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
here (h,k) is the center of the cirlce and (x,y) is the point on the circle.
In our case (h,k) is (-2,2)
so our circle equation is
[tex](x--2)^{2} + (y-2)^{2} = r^{2}[/tex]. ----------- (i)
and we can find our r by finding the distance between center and the point given on the circle. lets say we take (1,0) point given on the circle according to our diagram
Then
[tex]r = \sqrt{(-2-1)^{2}+(2-0)^{2}}[/tex]
[tex]r = \sqrt{9+4}[/tex]
[tex]r = \sqrt{13}[/tex]
so by putting the values of r in equation (i)
[tex](x--2)^{2} + (y-2)^{2} = \sqrt{13} ^{2}[/tex]
[tex](x+2)^{2} + (y-2)^{2} = 13[/tex]
Which is our third option.
