First plot the 4 points on graph paper:



By looking at the graph we can easily see that a circle can be drawn
through those 4 points and the center will be (h,k) = (4,3) and
the radius will be r=2.  Like this:





First we get the  center-radius form, which is



Substituting (h,k) = (4,3) and r=2





That's the center-radius form.

To get the general form which is



We start with the center-radius form which we just found,
remove the parentheses by squaring the binomials, collect 
like terms, get 0 on the right, and arrange in the 
general form:








If you know some short-cuts you can skip some of those steps.
But be careful.

Edwin