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 solve the problem, we need to find the locus of the point of intersection of the two given lines and show that it forms a hyperbola with an eccentricity of 2.

### Step 1: Write the equations of the lines
The equations of the lines are given as:
1. \( \sqrt{3}x - y - 4\sqrt{3}k = 0 \) (Equation 1)
2. \( \sqrt{3}kx + ky - 4\sqrt{3} = 0 \) (Equation 2)

### Step 2: Solve for the point of intersection
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