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 point of intersection of the lines y+mx=sqrt(a^(2)m^(2)+b^(2)) and my-x=sqrt(a^(2)+b^(2)m^(2)) is

Locus of points of intersection of lines x=at^(2),y=2at

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

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 ____________.

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.

Find the locus of the point of intersection of the lines sqrt(3x)-y-4sqrt(3 lambda)=0 and sqrt(3)lambda x+lambda y-4sqrt(3)=0 for different values of lambda.