Straight Lines L1

Straight Line L1

Straight Line L2

Straight Line L3

Show that the straight lines L_(1)=(b+c)x+ay+1=0,L_(2)=(c+a)x+by+1=0ndL_(3)=(a+b)x+cy+1 are concurrent.

In xy-plane, a straight line L_1 bisects the 1st quadrant and another straight line L_2 trisects the 2nd quadrant being closer to the axis of y . The acute angle between L_1 and L_2 is

The straight lines l_1, ,l_2 & l_3, are parallel & lie in the same plane. A total of m points are taken on the line l_1, n points on l_2, & k points on l_3. How many maximum number of triangles are there whose vertices are at these points ?

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, show that the locus of R as L varies, is a straight line