i'm so sorry.. i thought u wer asking the diameter.... i didnt see the word equation....
suppose the equation of the circle is x^2 + y^2 - 2gx - 2fy + c = 0 then.. centre of the circle is in (g,f) let the equation of the diameter be ax + by + k = 0 then... if you solve for x=g, y=f u'll get k..... all the solutions of the equation ag + bf + k = 0{ we have two variables a,b here but only one equation... so it is linear inequation} for a and b will represent different diameters of the circle....