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  • The locus of the point of intersection of lines square √3 x-y-4√3 k=0 and √3 kx+ky-4√3=0 for different value of k is a hyperbola whose eccentricity is 2.

The locus of the point of intersection of lines \sqrt{3}x-y-4\sqrt{3}k=0 and \sqrt{3}kx+ky-4\sqrt{3}=0 for different value of k is a hyperbola whose eccentricity is 2.

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True  

 Given equation of lines are \sqrt{3}x-y-4\sqrt{3}k=0

\sqrt{3}kx+ky-4\sqrt{3}=0

k=\frac{\sqrt{3}x-y}{4\sqrt{3}} andk=\frac{4\sqrt{3}}{\sqrt{3}x+y}

\frac{\sqrt{3}x-y}{4\sqrt{3}} =\frac{4\sqrt{3}}{\sqrt{3}x+y}

3x2-y2=48

\frac{x^{2}}{16}-\frac{y^{2}}{48}=1 which is the equation of hyperbola 

a2=16 and b2=48

e2=1+48/16=4

e=2

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