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Share/Save/Bookmark Login/ Register to Bookmark Topic : "14-10-09 Pair of straight lines bisect the angles from SL Loney" Started by Nishant

Nishant

#1 Posted 8:29pm 04-11-09  

14-10-09 Pair of straight lines bisect the angles from SL Loney

Prove that one of the lines represented by ax[p]3[/p]+bx[p]2[/p]y+cxy[p]2[/p]+dy[p]3[/p]=0 will bisect the angles between the other two if (3a+c)[p]2[/p](bc+2cd-3ad)=(b+3d)[p]2[/p](bc+2ab-3ad)


Source: SL Loney
-when spring comes, it melts the snow one flake at a time…    

Nishant

#2 Posted 10:00am 06-11-09  

Re: 14-10-09 Pair of straight lines bisect the angles from SL Loney

No one yet!
-when spring comes, it melts the snow one flake at a time…    

bubai

#3 Posted 00:31am 21-02-10  

Trial 1

We divide te above equation by x[p]3[/p].....
We get,
a+bm+cm[p]2[/p]+dm[p]3[/p]=0(as y=mx)
Using theory of sum and product of roots,
m[ss]1[/ss]+m[ss]2[/ss]+m[ss]3[/ss]=-b/a---------
and
m[ss]1[/ss]*m[ss]2[/ss]*m[ss]3[/ss]=-k/a-------
We get relation between slopes.
zxcvb    

johny

#4 Posted 00:33am 21-02-10  

Re: 14-10-09 Pair of straight lines bisect the angles from SL Loney

sir still u need the full proof?

by the way this is quite a standard one in many state board textbooks, isnt it ?
   
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