Straight Lines L1

Straight Line L1

Straight Line L2

Straight Line L3

Show that the straight lines L_1=(b+c)x+a y+1=0,\ L_2=(c+a)x+b y+1=0\ n d\ L_3=(a+b)x+c y+1=0\ are concurrent.

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.

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 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

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 ?