If two lines represented by `x^4+x^3y+c x^2y^2-x y^3+y^4=-` bisector of the angle between the other two, then the value of `c` is `0` (b) `-1` (c) 1 (d) `-6`

Options

A. 0
B. -1
C. 1
D. -6

Answer

4

Explanation

Since the product of the slope of the four lines represented by the given equation is 1 and a pair of lines represents the bisectors of the angles between the other two , the product of the slopes of each pairs is -1.
So , let the equation of one pairs be `ax^(2)+2hxy-ay^(2)=0`. then the equation of its bisectors is
`(x^(2)-y^(2))/(2a)=(xy)/(h)` By hypothesis ,
`x^(4)_x^(3)y+cx^(2)y^(2)-xy^(3)+y^(4)=(ax^(2)+2hxy-ay^(2))(hx^(2)-2axy-hy^(2))=ah(x^(4)+y^(4))+2(h^(2)-a^(2))(x^(3)y-xy^(3))-6ahx^(2)y^(2)`