A straight line L through the origin meets the lines `x + y = 1` and `x + y = 3` at P and Q respectively. Through P and Q two straight lines `L_1`, and` L_2` are drawn, parallel to `2x-y- 5` and `3x +y 5` respectively. Lines `L_1` and `L_2` intersect at R. Locus of R, as L varies, is

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio

A line L passing through (1, 1) intersect lines L_1: 12 x+5y=13 and L_2: 12 x+5y=65 at A and B respectively. If A B=5 , then line L can be

The equation of the straight line through the intersection of line 2x+y=1 and 3x+2y=5 passing through the origin, is:

If the lines L_1 and L_2 are tangents to 4x^2-4x-24 y+49=0 and are normals for x^2+y^2=72 , then find the slopes of L_1 and L_2dot

If the straight line x/a+y/b=1 passes through the line point of intersection of the lines x+y=3 and 2x-3y=1 and is parallel to x-y-6=0 , find a and b.

A given line L_1 cut x and y-axes at P and Q respectively and has intercepts a and b/2 on x and y-axes respectively. Let another line L_2 perpendicular to L_1 cut x and y-axes at R and S respectively. Let T be the point of intersection of PS and QR . Locus of T is a circle having centre at (A) (a, b) (B) (a, b/2) (C) (a/2, b) (D) (a/2, b/4)

A variable line L passing through the point B(2, 5) intersects the lines 2x^2 - 5xy+2y^2 = 0 at P and Q. Find the locus of the point R on L such that distances BP, BR and BQ are in harmonic progression.

Let L_1 be a straight line passing through the origin and L_2 be the straight line x + y = 1 if the intercepts made by the circle x^2 + y^2-x+ 3y = 0 on L_1 and L_2 are equal, then which of the following equations can represent L_1 ?

A variable line L drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that (OP)^(2) = OA . OB,

A straight line L through the point (3,-2) is inclined at an angle 60^@ to the line sqrt(3)x+y=1 . If L also intersects the x-axis then find the equation of L .