prove that the locus of the point of intersection of the lines root 3 x minus y - 4 root 3 k = 0 and root3kx + k y - 4 root 3 equals zero for different values of K is a hyperbola whose eccentricity is 2.....

12. Prove that the focus of the point of intersection of the lines $\sqrt{3}x-y-4\sqrt{3k}=0$ and $\sqrt{3}kx-ky-4\sqrt{3}=0$ for different values of k is a hyperbole whose eccentricity is 2.