Question

The difference of the tangents of the angles made by the lines 3x2 – 2xy –y2 = 0 with x-axis is

Answer 1

given equation is 3x^2 - 2xy - y^2 =0

3x^2 - 3xy + xy -y^2 = 0
3x(x-y) + y (x - y) =0
(3x +y)(x -y) =0
so the lines are 3x+y =0  and x-y = 0
i.e
y = -3x
and y = x
tangent of the angle made by a line with x axis is its slope.
so required difference is the difference of slopes which is  -3 -1 =-4  or 1-(-3) =  4