$A(a,0)$ and $B(-a,0)$ are two fixed points of triangle $ABC$. The vertex $C$ moves in such a way that $\cot A + \cot B = \lambda$,where $\lambda$ is a constant. Then the locus of the point $C$ is
- A$y\lambda = 2a$
- B$ya = 2\lambda$
- C$y = \lambda a$
- DNone of these
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