Step 1: Note down the equation and convert that equation into the standard form of the circle

NOTE: Standard form (x - h)^2 + (y - k)^2 = r^2

                      Where center  (h, k) and radius r  

              Skill 1: Take down the equation and separate the similar variables.

                          EXAMPLE: x^2 + y^2 - 6x + 4y = 12

                                             (x^2 - 6x) +(y^2 + 4y) = 12

            Skill 2: According signs of the equation convert these as

                        either (a+b)^2 \text{ or } (a-b)^2.

            Skill 3: Find out the a and b by convert the equation to

                         a^2 ± 2ab and compare.

                        EXAMPLE: [/math]x^2 - 6x[/math]

                                            a = x  

                              for b =?, take middle term - 6x = 2*3*x

                                              And compare it with the 2ab  

                                                      b = 3.

            Skill 4: Substitute the values of a and b in the formulas of (a±b)^2.            

              NOTE: Use the formulas of   (a+b)^2 \text{ or } (a-b)^2

                                       (a+b)^2 = a^2 + 2ab + b^2.

                                      a^2+2ab=(a+b)^2-b^2.

                                                      or

                                     a^2 - 2ab = (a-b)^2 - b^2 .

                        EXAMPLE:

                                        [math][(x-3)^2-9]+\left[\left(y+2\right)^2-4)\right]=12[/math]

                                        (x-3)^2+(y+2)^2=12+9+4

                                          (x-3)^2+(y+2)^2=25

Step 2: Note down the given  circle equation

            EXAMPLE: (x -2)^2 + (y + 1)^2 = \frac{169}{4}

Step 3: Compare the given equation with the Standard Form of circle equation.

          EXAMPLE: [math](x-2)^2+\left[y-\left(-1\right)\right]^2=\frac{169}{4}[/math] Compare it with

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

          Where center  (h, k) and radius r  

Step 4: Identify the r, h and k values.

            NOTE: r- radius

                        h is x-coordinate

                        k is y- coordinate of the center.

          EXAMPLE; (h, k) = (2, -1), r = \frac{168}{4}