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Grade 12th passAnalytical Geometry

Find an equation of the angle bisector of the obtuse angles formed by the lines 2x+6y= 9 and x-3y= -2. sketch the given lines and angle bisector.

Profile image of ian dave advincula
11 Years agoGrade 12th pass
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1 Answer

Profile image of Nishant Vora
11 Years ago
Hi student,

2x+6y + 9 =0 and x-3y + 2 =0
so a1a2 + b1b2 = 2*1 + 6*(-3) = 2 – 18 = -16 <0

So negative sign will give me obtuse angle bisector

So
\frac{2x+6y + 9}{\sqrt{2^2 + 6^2}} = - \frac{(x-3y + 2 )}{\sqrt{1^2 + (-3)^2}}
Now you can simplify the above

Concept is SIGN OF a1a2 + b1b2 WILL GIVE ME THE EQUATION OF OBTUSE ANGLE BISECTOR

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