You can use the equation of the circle with center at (h,k) and the radius of f units.
The correct option for the given condition is
Option C: [tex](x-4)^2 + (y-5)^2 = 4\\[/tex]
If a circle has center at (h,k) and radius is of r units, then its equation is given as
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Since the graphed circle has center at x = 4 and y = 5, thus we have
(h,k) = (x coordinate of center, y coordinate of center ) = (4,5)
And since the radius of the needed circle is needed to be of 2 units, thus,
r = 2 units
Using the above specified formula, we get the equation of the needed circle as
[tex](x-h)^2 + (y-k)^2 = r^2\\(x-4)^2 + (y-5)^2 = 2^2 = 4\\\\(x-4)^2 + (y-5)^2 = 4\\[/tex]
Thus,
The correct option for the given condition is
Option C: [tex](x-4)^2 + (y-5)^2 = 4\\[/tex]
Learn more about equation of circles here:
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