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  • Equation of the bisector of obtuse angle between the lines <img alt="\mathrm{3 x-4 y+7=0 \: and \: 12 x+5 y-2=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x-4%20y&pl

Equation of the bisector of obtuse angle between the lines \mathrm{3 x-4 y+7=0 \: and \: 12 x+5 y-2=0} is -
 

Option: 1

\mathrm{11 x+3 y-9=0}


 


Option: 2

11 \mathrm{x}-3 \mathrm{y}+9=0
 


Option: 3

21 \mathrm{x}-77 \mathrm{y}+101=0
 


Option: 4

21 \mathrm{x}+77 \mathrm{y}-101=0


Answers (1)

best_answer

Equation of bisector is
\mathrm{ \frac{3 x-4 y+7}{5}= \pm \frac{(12 x+5 y-5)}{13} }

i.e \mathrm{21x+77y-101=0,11x-3y+9=0}

Now slope of \mathrm{3 x-4 y+7=0\: is \: m 1=\frac{3}{4}. Slope\: of \: 11 x-3 y+9=0\: is \: m\: 2=\frac{11}{3}}

If \mathrm{\theta} be the angle between lines then \mathrm{\tan =\left|\frac{\frac{11}{3}-\frac{3}{4}}{1+\frac{11}{4}}\right|=\frac{35}{45}<1}

Thus equation of obtuse angle bisector is \mathrm{21 \mathrm{x}+77 \mathrm{y}-101=0.}

Hence option 4 is correct.

Posted by

Kuldeep Maurya

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