39sir still u need the full proof?
by the way this is quite a standard one in many state board textbooks, isnt it ?
Prove that one of the lines represented by ax3+bx2y+cxy2+dy3=0 will bisect the angles between the other two if (3a+c)2(bc+2cd-3ad)=(b+3d)2(bc+2ab-3ad)
Source: SL Loney
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3 Answers
1We divide te above equation by x3.....
We get,
a+bm+cm2+dm3=0(as y=mx)
Using theory of sum and product of roots,
m1+m2+m3=-b/a---------
and
m1*m2*m3=-k/a-------
We get relation between slopes.
39