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

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 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 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. Then find the vertex 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 l and m are variable real numbers such that 5l^2-4lm+6m^2+3l=0 , then the variable line lx+my=1 always touches a fixed parabola, whose axis is parallel to the X-axis. If (c,d) is the focus of the parabola , then the value of 2^|d-c| is

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

Prove that the equation y^2+ 2Ax + 2By +c =0 represents a parabola whose axis is parallel to the x-axis.

Find the differential equation of all parabolas whose axis are parallel to the x-axis.