If Two Of The Lines Represented By                         x4 + x3 y + cx2 y2 – xy3 + y4 = 0   Bisect The Angle Between The Other Two, Then The Value Of c is 

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If two of the lines represented by  

                      x4 + x3 y + cx2 y2 – xy3 + y4 = 0  

bisect the angle between the other two, then the value of c is 


Correct option is

– 6

Since the product of the slopes of the four lines represented by the given equation is 1 and a pair of lines represent the bisectors of the angles between the other two, the product of the slopes of each pair is –1. So let the equation of one pair be

ax2 + 2hxy – ay2 = 0.  


By hypothesis

            x4 + x3y + cx2y2 – xy3 + y4  



Compairing the respective co-efficients we get

           ah = 1 and c = –6ah = –6 



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