Question

Which of the following is a result of shifting a circle with equation (x - 5)^2 + (y - 6)^2 = 36 to the right 2 units?

Answer 1

C. The x-coordinate of the center of the circle increases by 2.
Because the equation of a circle is:
(x-h)^2 + (y-k)^2 = r^2, where the center of the circle is at (h, k), and the radius of the circle = r
So the center of this circle is at (5, 6).
To shift it to the right 2 units means to make the center 5+2=7, with no change in y or r.

Answer 2

Recall,

Circle centered at (h,k) and radius r --

$(x-h)^2+(y-k)^2=r^2$

Here it is a circle centered at (h,k)=(5,6) and radius r=6
If you move to the right, the x coordinate will increase, so here the only change is the x coordinate increases by 2.
$(x-5)^2+(y-6)^2=r^2$
$(x-7)^2+(y-6)^2=6^2$