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What is the equation of acute angle bisector of the lines y = 0 and \sqrt 3 x -y = 0

Option: 1

x + \sqrt 3 y = 0


Option: 2

x - \sqrt 3 y = 0


Option: 3

\sqrt 3x + y = 0


Option: 4

None of these 


Answers (1)

best_answer

The given lines are

y = 0, so a1 = 0, b1 = 1

\sqrt 3 x -y = 0,  a2 = \sqrt 3, b2 = - 1

So a1a2 + b1b2  = -1 < 0

So negative sign will give obtuse bisector and positive sign will give acute bisector

Hence, the equation of acute bisector is 

\\\frac{y}{1}= +\frac{\sqrt{3}x - y}{2}\\\\\sqrt{3}y = x

 

Alternate Method 

One of the lines is x-axis, and the other line is represented by V in the figure

The two possible bisectors are represented by dotted lines

Clearly, the acute angle bisector makes the angle of 60o with x - axis

So, m = \tan \theta = 1/ \sqrt 3

It also passes from origin

So, its equation is y = x/ \sqrt 3 

 x = \sqrt 3 y

 

 

Posted by

vinayak

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