`sqrt3kx + ky=4sqrt3`
`sqrt3x - y=4sqrt3k`
The locus of the point of intersection of these lines form a conic with eccentricity _______

If sqrt3x - 2=2sqrt3 + 4 , then the value of x is

sqrt(7+4sqrt3) - sqrt(7-4sqrt3) =

The locus of point of intersection of the lines y+mx=sqrt(4+m^(2)) and my-x=sqrt(1+4m^(2)) is x^(2)+y^(2)=k then "k" is

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 ____________.

(sqrt(8)-sqrt(3))(-4+sqrt(3))

A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of 4sqrt(3) units from their point of intersection.The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (a) (-(2)/(sqrt(3)),2) (b) (0,0) (c) ((2)/(sqrt(3)),2) (d) (0,4)

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.

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