Questions

# The line 3x-3y+17=0 bisects the angle between a pair of lines of which one line is 2x+y+4=0, then the equation to the other line is

## Remember concepts with our Masterclasses.

80k Users
60 mins Expert Faculty Ask Questions
a
$3x+6y-5=0$
b
$3x+6y-7=0$
c
$7x-y+14=0$
d
$4x-y+3=0$

## Ready to Test Your Skills?

Check Your Performance Today with our Free Mock Tests used by Toppers!

detailed solution

Correct option is A

$\begin{array}{l}Let\text{\hspace{0.17em}}\mathrm{Re}quired\text{\hspace{0.17em}}Equation\text{\hspace{0.17em}}y-\frac{22}{9}=m\left(x+\frac{29}{9}\right)--\left(3\right)\\ If\text{\hspace{0.17em}}\left(1\right)\text{\hspace{0.17em}\hspace{0.17em}}is\text{\hspace{0.17em}\hspace{0.17em}}angle\text{\hspace{0.17em}}bi\mathrm{sec}tor\text{\hspace{0.17em}}of\text{\hspace{0.17em}}\left(2\right)&\left(3\right)\text{\hspace{0.17em}\hspace{0.17em}}then\\ Angle\text{\hspace{0.17em}}b/w\text{\hspace{0.17em}}\left(1\right)&\left(3\right)=\text{\hspace{0.17em}}Angle\text{\hspace{0.17em}}b/w\text{\hspace{0.17em}}\left(1\right)&\left(2\right)\\ \therefore \text{\hspace{0.17em}}|\frac{m-1}{1+m}|=|\frac{1+2}{1-2}|\\ ⇒\text{\hspace{0.17em}}|\frac{m-1}{1+m}|=3\\ If\text{\hspace{0.17em}}\frac{m-1}{1+m}=3,If\text{\hspace{0.17em}}\frac{m-1}{1+m}=-3\\ ⇒\text{\hspace{0.17em}}m-1=3+3m,⇒\text{\hspace{0.17em}}m-1=-3-3m\\ ⇒\text{\hspace{0.17em}}2m=-4,⇒\text{\hspace{0.17em}}4m=-2\\ ⇒\text{\hspace{0.17em}}m=-2,⇒\text{\hspace{0.17em}}m=-1}{2}\end{array}$

$\begin{array}{l}\therefore \text{\hspace{0.17em}}m=-1}{2}\text{\hspace{0.17em}\hspace{0.17em}}from\text{\hspace{0.17em}}\left(3\right)\\ y-\frac{22}{9}=\frac{-1}{2}\left(x+\frac{29}{9}\right)\\ ⇒\text{\hspace{0.17em}}2\left(9y-22\right)=-\left(9x+29\right)\\ ⇒\text{\hspace{0.17em}}18y-44=-9x-29\\ ⇒\text{\hspace{0.17em}}9x+18y-15=0\\ ⇒\text{\hspace{0.17em}}3x+6y-5=0\end{array}$

test your
knowledge
5 Questionscheck how much you know about a topic
5 minsstand a chance to win up-to 100% scholarships

Talk to our academic expert!

+91

Are you a Sri Chaitanya student?

Create Your Own Test
Your Topic, Your Difficulty, Your Pace