Consider two lines l1: 3x-2y-12=0 l2: 2x+y+6=0, family of curves passing through points of intersections of these two lines with x and y axes is (3x-2y-12)(2x+y+6)+(lambda)xy=0 . This family clearly, always passes through 3 fixed (non-collinear) points (-3,0) (4,0) (0,-6). But the equation(of family) itself can never be a circle for any lambda. I can't figure out where I am going wrong. Please help me out with this.
Thanks in advance.