A and B are two fixed points in a ΔABC  If its vertex C moves in such a way that cotA+cotB=λ  where λ  is constant. Then the locus of the point C is

We may suppose that coordinates of two fixed points A,B are (a,0)  and   (−a,0)  respectively and coordinates of the variable point C are (h,k)In ΔCDA   cotA=DACD=a−hk  andIn ΔDBC,           cotB=BDCD=a+hkBut                    cotA+cotB=λSo we have       a−hk+a+hk=λ⇒                  2ak=λ   ⇒    2a=kλ∴  Locus of C is λy=2a  or  y=2aλ.