State whether the following statement is True or False : The locus of the point of intersection of lines $\sqrt 3x-y-4\sqrt 3k=0$ and $\sqrt 3kx+ky-4\sqrt 3=0$ for different value of $k$ is a hyperbola whose eccentricity is 2.

Question

[Hint : Eliminate $k$ between the given equations]

$\begin{array}{1 1}\text{True}\\\text{False}\end{array} $