A straight lines 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. Line `L_1` and `L_2` intersect at R. Show that the locus of R as L varies is a straight line.

A straight line through the point A (-2,-3) cuts the line x+3y=9 and x+y+1=0 at B and C respectively. If AB.AC =20 then equation of the possible line 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) 1:2 (B) 3:2 (C) 2:1 D) 4:3

The line y=(3x)/4 meets the lines x-y+1=0 and 2x-y=5 at A and B respectively. Find Coordinates of P on y=(3x)/4 such that PA*PB=25.

Let a given line L_1 intersect the X and Y axes at P and Q respectively. Let another line L_2 perpendicular to L_1 cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

The points P(h,k) and Q (k,h) lie on the respective lines 6x-y=1and2x-5y=5 , find the equation of the straight line Pq.

A line intersects the straight lines 5x-y-4=0 and 3x-4y-4=0 at A and B , respectively. If a point P(1,5) on the line A B is such that A P: P B=2:1 (internally), find point Adot

A straight line is perpendicular to the straight line 3x-4y=6 and passes through (2,1) . Find its equation.

A straight lines L through the point ( 3, 2) is inclined at an angle 60^@ to the line sqrt3x +y =1 . If L also intersects the x-axis, then the equation of L is

Consider two lines L_1a n dL_2 given by a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0, intersecting at point PdotA line L_3 is drawn through the origin meeting the lines L_1a n dL_2 at Aa n dB , respectively, such that PA=P B . Similarly, one more line L_4 is drawn through the origin meeting the lines L_1a n dL_2 at A_1a n dB_2, respectively, such that P A_1=P B_1dot Obtain the combined equation of lines L_3a n dL_4dot

The straight line 4x + 3y - 12 = 0 intersects the x -and y-axis A and B respectively. Find the coordinates of the point at which the straight line bar(AB) is divided internally into the ratio 2 : 1.