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.

Prove that the locus of the point of iter section of the lines sqrt3x-y-4sqrt3k=0 and sqrt3kx+ky=4sqrt3 for different values of'k is hyperbola whose eccentricity is 2

The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 t= 0 & sqrt3 tx +ty-4 sqrt3=0 (where t is a parameter) is a hyperbola whose eccentricity is:

The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 t= 0 & sqrt3 tx +ty-4 sqrt3=0 (where t is a parameter) is a hyperbola whose eccentricity is: (a) sqrt3 (b) 2 (c) 2/sqrt3 (d) 4/3

sqrt(3)x^(2) - sqrt(2)x + 3sqrt(3)=0

Find the angle between the lines y-sqrt3 x - 5 = 0 and sqrt3 y -x + 6 = 0

Solve for x : sqrt3x^2 - 2sqrt2x - 2sqrt3 = 0

The triangle formed by the line x+sqrt3y=0, x- sqrt3y=0 and x=4 is-

If the lines 2x + y - 3 = 0 , 5x + ky - 3 = 0 " and " 3x - y - 2 = 0 are concurrent , find the value of k.

The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

The hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 passes throught the point of intersection of the lines x - 3sqrt(5)y =0 and sqrt(5)x - 2y = 13 and the length of its latus rectum is (4)/(5) . Find the coordinates of its foci.