Answer:
The circles do intersect.
Step-by-step explanation:
A circle is of the form
(x-h)^2+(y-k)^2=r^2
where,
h = Point on x axis of the circle center
k = Point on y axis of the circle center
[tex]x^2+y^2=4\\\Rightarrow (x-0)^2+(y-0)^2=2^2[/tex]
So, the center of the circle is at (0,0) and radius is 2 units
[tex]x^2-4x+y^2-4y+4=0\\\Rightarrow (x^2-4x)+(y^2-4y)=-4\\\Rightarrow (x-2)^2+(y-4)^2=-4\\\Rightarrow (x^2+4-4x)+(y^2+4-2y)=-4\\\Rightarrow (x-2)^2+(y-2)^2=-4+4+4\\\Rightarrow (x-2)^2+(y-2)^2=4\\\Rightarrow (x-2)^2+(y-2)^2=2^2[/tex]
The circle center is at the point (2,2) and radius is 2 units.
Hence, the circles do intersect.
