If l and m are variable real number such that `5l^(2)+6m^(2)-4lm+3l=0`, then the variable line lx+my=1 always touches a fixed parabola, whose axes is parallel to the x-axis.
The directrix of the parabola is

If l and m are variable real number such that 5l^(2)+6m^(2)-4lm+3l=0 , then the variable line lx+my=1 always touches a fixed parabola, whose axes is parallel to the x-axis. The focus of the parabola is

If l,m are variable real numbers such that 5l^2+6m^2 -4lm+3l=0 and the variable line lx + my = 1 always touches a fixed parabola P(x,y) = 0 whose axis parallel to x-axis , then A) vertex of P(x,y) is (-5/3, 4/3) B) Latus Rectum is equal to 4 C) Directrix of P(x,y) is parallel to y-axis (D) AB is a focal chord of P(x,y) =0 then 1/(SA)+1/(SB)=1/2 where S is the focus

If 2p^(2)-3q^(2)+4pq-p=0 and a variable line px+qy=1 always touches a parabola whose axis is parallel to x -axis then.Then equation of parabola is

The line lx+my+n=0 touches y^(2)=4ax

Consider the relation 4l^(2)-5m^(2)+6l+1=0 , where l, m inR . The line lx+my+1=0 touches a fixed circle whose equation is

A parabola of latus rectum l touches a fixed equal parabola.The axes of two parabolas are parallel.Then find the locus of the vertex of the moving parabola.

Factorize (l+m)^(2)-4lm