find the equation of a circle which passes through the origin and cuts off chords of length 4 and 6 on the positive x axis and y axis resp

let equation of circle be x^2 +y^2 +2gx+2fy+c.............eq1

 as circle passes through origen therefore c=0

 x intersept is given by 2(g^2-c)^1/2 =4

 y intersept is given by 2(f^2-c)^1/2 =6

  we get (g,f)=(+_2,+_3)

   now eq1 becomes

                              x^2 + y^2  +_4x  +_6y =0 is the required circle