Home
Class 12
MATHS
If l,m are variable real numbers such ...

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

Promotional Banner

Similar Questions

Explore conceptually related problems

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 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

A parabola with vertex (2,3) and axis parallel toy-axis,passes through (4,5). Then length of its latus rectum is

The value of k such that the line 3x+4y+5-k(x+y+3)=0 is parallel to y-axis is

Equation of a parabola whose vertex is (2,-3), axis is parallel to the x axis and latus rectum 8 is

Find the equation of the parabola whose vertex is at (2,-3), axis is parallel to x -axis and length of latus rectum is 12

The equation y^2+3=2(2x+y) represents a parabola with the vertex at: (1/2,1) & axis parallel to x-axis (1,1/2) & axis parallel to x-axis (1/2 , 1) & focus at (3/2,1) (1/2,1) & axis parallel to y-axis.