The locus of the point of intersection of lines `sqrt3x-y-4sqrt(3k)`=0 and `sqrt3kx+ky-4sqrt3=0` for different value of k is a hyperbola whose eccentricity is 2.

Explanation

To find the locus of the point of intersection of the lines given by the equations \( \sqrt{3}x - y - 4\sqrt{3}k = 0 \) and \( \sqrt{3}kx + ky - 4\sqrt{3} = 0 \) for different values of \( k \), we will follow these steps:

### Step 1: Express \( k \) in terms of \( x \) and \( y \) from the first equation.
From the first equation:
\[ \sqrt{3}x - y - 4\sqrt{3}k = 0 \]
Rearranging gives:
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