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

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

For the variable t , the locus of the points of intersection of lines x - 2y = t and x + 2y = (1)/(t) is _

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

The locus of lhe point of intersection of the lines x+4y=2a sin theta,x-y=a cos theta where theta is a variable parameter is

For the variable t, the locus of the points of intersection of lines 3tx-2y+6t=0 and 3x+2ty-6=0 is

The equation to the locus of point of intersection of lines y-mx=sqrt(4m^(2)+3) and my+x=sqrt(4+3m^(2)) is

Find the locus of the point of intersection of the lines x=a/(m^(2)) and y=(2a)/(m) , where m is a parameter.

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

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