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Analytical Geometry

Blazing goIITian

Joined:	31 Jan 2007
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9 Apr 2008 14:34:02 IST

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451

IIT-2004 Q

None

area of triangle formed by the angle bisectors of the pair of lines

x² -y²+2y-1=0 and the line x+y=3 is:

a)1 b)2 c)3 d)4

my doubt is how to find the eqn of the bisectors???????

plz reply soon

rates assured.

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Comments (7)

Ambareesh Rishi

Blazing goIITian

Joined: 4 May 2007

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9 Apr 2008 14:44:40 IST

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answer is 2

varsha valli g.

Blazing goIITian

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9 Apr 2008 14:45:57 IST

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thats right but how did u find the eqn of the bisectors????pl xplain
!!!!!!!!!!

Ambareesh Rishi

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9 Apr 2008 14:50:16 IST

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tlet the linew be

ax + by +c and ax1+by1+c1

then equation of bisectors

(ax+by+c)/root(a*a+b*b) =+or - (ax1+by1+c1)/root(a1*a1+b1*b1)

one will give the equation of the acute angle and other will give the equation of the obtuse angle bisector

varsha valli g.

Blazing goIITian

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9 Apr 2008 15:02:54 IST

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thta is the case when the 2 eqns of the lines r given,but here combined eqn is given ,how did uu split it up.
xplain!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!plz

joy francis

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9 Apr 2008 16:12:56 IST

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x² -y²+2y-1=0 is the joint eqn of

x-y+ 1 = 0 &

x+y-1 = 0..

ankit aggarwal

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9 Apr 2008 17:29:34 IST

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let a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 are the lines.
then the procedure to find the angle bisectors is

1) make c₂&c₂ positive.

2)if a₁a₂+b₁b₂>0
=> (a₁x+b₁y+c₁)/root(a₁²+a_2²) =+ (a₂x+b₂y+c₂)/root(a₂²+b_2²)
is obtuse angle bisector

=>(a₁x+b₁y+c₁)/root(a₁²+a_2²) =- (a₂x+b₂y+c₂)/root(a₂²+b_2²)
is acute angle bisector
-----------------------------------------
if a₁a₂+b₁b₂<0
=> (a₁x+b₁y+c₁)/root(a₁²+a_2²) =+ (a₂x+b₂y+c₂)/root(a₂²+b_2²)
is acute angle bisector

=>(a₁x+b₁y+c₁)/root(a₁²+a_2²) =- (a₂x+b₂y+c₂)/root(a₂²+b_2²)
is obtuse angle bisector

Conjurer

Blazing goIITian

Joined: 20 Feb 2008

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9 Apr 2008 17:48:33 IST

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Some additional info:

Equations of the bisectors of the angles between two lines represented by ax^2 + 2hxy + by^2 + 2gx + 2fy + c=0 are given by

(x-x1)^2 - (y-y1)^2/a-b = (x-x1)(y-y1)/h

where(x1,y1) is the point of intersection of the lines represented by the given equation.

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