Show that the pairs of straight lines `2x^2+6x y+y^2=0` and `4x^2+18 x y+y^2=0` have the same set of angular bisector.

If the pairs of straight lines x^(2) - 2pxy-y^(2)=0 and x^(2) – 2qxy - y^(2) = 0 be such that each pair bisects the angle between the other pair, then

Show that the straight line x^2-4xy+y^2=0 and x + y = 3 form an equilateral triangle.

The equation of a line which is parallel to the line common to the pair of lines given by 6x^2-x y-12 y^2=0 and 15 x^2+14 x y-8y^2=0 and at a distance of 7 units from it is (a) 3x-4y=-35 (b) 5x-2y=7 (c) 3x+4y=35 (d) 2x-3y=7

Show that the straight line x-2y+3=0 and 6x+3y+8=0 are perpendicular .

If the pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by (a) 3x^2+8x y-3y^2=0 (b) 3x^2+10 x y+3y^2=0 (c) y^2+2x y-3x^2=0 (d) x^2+2x y-3y^2=0

Show that the traingle formed by staright lines 4x-3y-18=0,3x-4y+16=0and x+y-2=0 is isosceles

If the pairs of lines x^(2) – 2nxy - y^(2) = 0 and x^(2) – 2mxy - y^(2) = 0 are such that one of them represents the bisectors of the angles between the other, then

The distance between the pair of parallel lines x^(2) + 4xy + 4y^(2) + 3x + 6y- 4 = 0 is