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

The lines (lx+my)^2-3(mx-ly)^2=0 and lx+my+n=0 forms

Show that the line lx+my+n=0 is a normal to the circles S=0 iff gl+mf=n .

The direction cosines of two lines satisfying the conditions l + m + n = 0 and 3lm - 5mn + 2nl = 0 where l, m, n are the direction cosines. Angle between the lines is

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.

The direction cosines of two lines satisfying the conditions l + m + n = 0 and 3lm - 5mn + 2nl = 0 where l, m, n are the direction cosines. The value of lm+mn + nl is

The condition for the lines lx+my+n=0 and l_(1)x+m_(1)y+n_(1)=0 to be conjugate with respect to the circle x^(2)+y^(2)=r^(2) is

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

If the segment intercepted by the parabola y^2=4a x with the line l x+m y+n=0 subtends a right angle at the vertex, then 4a l+n=0 (b) 4a l+4a m+n=0 4a m+n=0 (d) a l+n=0

The direction cosines l, m and n of two lines are connected by the relations l+m+n=0 and lm=0 , then the angle between the lines is

the acute angle between two lines such that the direction cosines l, m, n of each of them satisfy the equations l + m + n = 0 and l^2 + m^2 - n^2 = 0 is