Prove that the lines `2x^2+6xy+y^2=0` are equally inclined to the lines `4x^2+18xy+y^2=0`

Show that the pair of lines given by a^2x^2+2h(a+b)xy+b^2y^2=0 is equally inclined to the pair given by ax^2+2hxy+by=0 .

If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y= mx + 4, find the value of m.

The equation of the circle which touches the circle x^2+y^2-6x+6y+17 = 0 externally and to which the lines x^2-3 xy-3x + 9y = 0 are normals, is

Prove that st. line 5x -2y - 1 = 0 is mid-parailel to the st. lines : 5x - 2y -9 =0 and 5x - 2y + 7 = 0.

Find the condition that one of the lines given by ax^2+2hxy+by^2=0 may coincide with one of the lines given by a' x^2 +2h'xy+b'y^2=0

The factors of 9x^2 + 6xy + y^2 are :

The lines represented by x^(2)+2lambda xy+2y^(2)=0 and the lines represented by (1+lambda)x^(2)-8xy+y^(2)=0 are equally inclined, then lambda =

Prove that the bisectors of the angle between the lines ax^2+acxy+cy^2=0 and (3+1/c)x^2+xy+(3+1/a)y^2=0 are always the same .

Find the equation of the line perpendicular to the line 2x+y -1 = 0 through the intersection of the lines x+2y -1= 0 and y=x.