[" The locus of a point of intersection of two lines "x sqrt(3)-y=k sqrt(3)" and "],[sqrt(3)kx+ky=sqrt(3),k in R," describes "]

Prove that the locus of the point of intersection of the lines sqrt(3) x-y-4sqrt(3) k=0 and sqrt(3) kx + ky-4sqrt(3) = 0 for different values of k is a hyperbola whose eccentricity is 2.

Prove that the locus of the point of intersection of the lines sqrt(3)x - y - 4 sqrt(3)k = 0 and sqrt(3)kx + ky - 4sqrt(3) = 0 for differenet values of k is a hyperbola whose eccentericity is 2.

The locus of the point of intersection of the lines sqrt(3)x-y-4sqrt( 3) k =0 and kxsqrt(3) +ky -4sqrt(3) =0 is a hyperbola of eccentricity

The locus of the point of intersection of the lines (sqrt(3))kx+ky-4sqrt(3)=0 and sqrt(3)x-y-4(sqrt(3))k=0 is a conic, whose eccentricity is ____________.

The locus of the point of intersection of the 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.

The locus of the point of intersection of the lines, sqrt(2)x-y+4sqrt(2)k=0" and "sqrt(2)kx+ky-4sqrt(2)=0 (k is any non-zero real parameter), is:

The locus of the point of intersection of the lines, sqrt(2)x-y+4sqrt(2)k=0" and "sqrt(2)kx+ky-4sqrt(2)=0 (k is any non-zero real parameter), is:

Locus of the point of intersection of the lines mx sqrt(3) + my - 4sqrt(3) = 0 and xsqrt(3) - y - 4 msqrt(3) = 0 , where m is parameter , is