Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

If the line l_{1}: 3 \mathrm{y}-2 \mathrm{x}=3  is the angular bisector of the line l_{2}: \mathrm{x}-\mathrm{y}+1=0 and l_{3}: \mathrm{ax}+\beta \mathrm{y}+17, then \alpha^{2}+\beta^{2}-\alpha-\betais equal to_______.

 

Option: 1

348


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Point of intersection of \ell_{1}: 3 y-2 x=3

\ell_{2}: \mathrm{x}-\mathrm{y}+1=0$ is $\mathrm{P} \equiv(0,1)

Which lies on \ell_{3}: \alpha x-\beta y+17=0,

\Rightarrow \beta=-17

Consider a random point \mathrm{Q} \equiv(-1,0)

on \ell_{2}: \mathrm{x}-\mathrm{y}+1=0, image of \mathrm{Q} about

\ell_{2}: \mathrm{x}-\mathrm{y}+1=0$, is $\mathrm{Q}^{\prime} \equiv\left(\frac{-17}{13}, \frac{6}{13}\right) which is calculated by formulae

\frac{\mathrm{x}-(-1)}{2}=\frac{\mathrm{y}-0}{-3}=2\left(\frac{-2+3}{13}\right)

Now, Q^{\prime}$ lies in $\ell_{3}: \alpha \mathrm{x}+\beta \mathrm{y}+17=0
\Rightarrow \alpha=7
Now, \alpha^{2}+\beta^{2}-\alpha-\beta=348

Posted by

SANGALDEEP SINGH

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

NTA JEE Main Admit Card 2025 LIVE: Session 2 hall ticket for BE, BTech soon; IIT, NIT cut-offs
anam-khan

JEE Main 2025: BTech ECE cut-offs for female candidates go up at top NITs
anam-khan

JEE Main 2025 Session 2 City Slip (OUT) Live: Admit card likely on March 29 at jeemain.nta.nic.in; cut-offs

Latest Question