What type of conic section is the following equation? x2 + (y - 5)2 = 12

A circle has equation
  (x -h)^2 +(y -k)^2 = r^2

Your equation matches this with h=0, k=5, r=2√3.

The given equation is that of a circle of radius 2√3 centered at (0, 5).

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Since your exponents are shown without the appropriate indicator (^), we cannot tell if your "12" is supposed to be "twelve" or "one squared". We have assumed "twelve." If it is "one squared", the radius is 1, not 2√3.