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.

The locus of the point of intersection of lines `sqrt3x-y-4sqrt(3k)`=0

1.	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.
Answer» True Given equation of line are `sqrt3x-y-4sqrt3k`=0 …(i) and `sqrt3kx+ky-4sqrt3=0` From Eq. (i) `4sqrt3k=sqrt3x-y` `rArr k=(sqrt3x-y)/(4sqrt3)`put in Eq. (ii), we get `sqrt3x((sqrt3x-y)/(4sqrt3))+((sqrt3x-y)/(4sqrt3))y-4sqrt3=0` `rArr1/4(sqrt3x^(2)-xy)+1/4(xy-(y^(2))/(sqrt3))-4sqrt3=0` `rArr (sqrt3)/4x^(2)-(y^(2))/(4sqrt3)-4sqrt3=0` `rArr 3x^(2)-y^(2)-48=0` `rArr 3x^(2)-y^(2)=48`,which is hyperbola.

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