Let (h,k) be the intersection point of tangent. Then the chord of the tangent is the common chord of the circles x2+y2=12 and x2−y2−5x+3y−2=0 Consider the diagram,
The equation of the common chord is, 5x−3y−10=0 The equation of the common chord is, 5x−3y−10=0⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) The equation of common chord of contact is hx+ky−12=0⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) The equation (I) and (II) represents the same line so,