Answer:
Option B.
Step-by-step explanation:
Consider the below figure attached with this question.
From the below figure it is clear that the center of the given circle is (4,5).
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, (h,k) is center of the circle and r is radius.
We need to find the equation of a circle which represents the same center as the circle shown but with a radius of 2 units.
Substitute h=4, k=5 and r=2 in the above equation.
[tex](x-4)^2+(y-5)^2=(2)^2[/tex]
[tex](x-4)^2+(y-5)^2=4[/tex]
The required equation is [tex](x-4)^2+(y-5)^2=4[/tex].
Therefore, the correct option is B.
