Prove that the locus of the point of intersection of the lines `sqrt3 x -y -4 sqrt3 k =0 and sqrt3 k x+ ky - 4 sqrt3 =0,` for different values of k, is a hyperbola whose eccentricity is 2.

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 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:

Find the locus of the point of intersection of the lines sqrt(3x)-y-4sqrt(3lambda)=0a n dsqrt(3)lambdax+lambday-4sqrt(3)=0 for different values of lambdadot

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

The locus of the point of intersection of the lines sqrt(3)x-y-4sqrt(3)lambda=0\ a n d\ sqrt(3)lambdax+lambday-4sqrt(3)=0 is a hyperbola of eccentricity a. 1 b. 2 c. 3 d. 4

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:

Solve sqrt3 x^2 + x + sqrt3 = 0

(v) Solve for x and y if (sqrt2 x+sqrt 3 y)=0 and (sqrt3 x- sqrt8 y)=0

Prove that the diagonals of the parallelogram formed by the lines sqrt(3)x+y=0, sqrt(3) y+x=0, sqrt(3) x+y=1 and sqrt(3) y+x=1 are at right angles.

Distance of origin from the line (1+sqrt3)y+(1-sqrt3)x=10 along the line y=sqrt3x+k