The diagonals of the parallelogram whose sides are `lx+my+n = 0`,`lx+ my+ n',=0`, `mx+ly+n=0`, `mx+ly+n'=0` include an angle

The diagonals of the parallelogram whose sides are lx+my+n=0, lx+my+n_(1)=0, mx+ly+n=0, mx+ly=n_(1)=0 include an angle

The diagonals of the parallelogram whose sides are lx+m y+n=0, l x+m y+n^(prime)=0 m x+l y+n=0, m x+l y+n^(prime)=0 include an angle

If the lines lx + my + n = 0, mx + ny + l = 0 and nx + ly + m = 0 are concurrent then

Show that the lines lx + my + n = 0 , mx + ny + l = 0 and nx + ly + m = 0 are concurrent, if l + m + n = 0.

A triangle is formed by the straight lines ax + by +c = 0, lx + my + n = 0 and px+qy + r = 0 . Show that the straight line : (px+qy+r)/(ap+bq) = (lx+my+n)/(al+mb) passes through the orthocentre of the triangle.

Factoris the expression. lx + my + mx + ly