The condition for the lines (l x+m y+n=0) and (l\_{1} x+m\_{... | Mathematics | SolveeIt | Solveeit

Today, August 23

Question

The condition for the lines $l x+m y+n=0$ and $l_{1} x+m_{1} y+n_{1}=0$ to be conjugate with respect to the circle $x^{2}+y^{2}=r^{2}$ , is

A

$r^{2}\left(ll_{1}+m m_{1}\right)=n n_{1}$

B

$r^{2}\left(ll_{1}-m m_{1}\right)=n n_{1}$

C

$r^{2}\left(ll_{1}+m m_{1}\right)+n n_{1}=0$

D

$r^{2}\left(l m_{1}+l_{1} m\right)=n n_{1}$

Answer

$r^{2}\left(ll_{1}+m m_{1}\right)=n n_{1}$

Explanation

Solution

Condition for conjugate line is $r^{2}\left(ll_{1}+m m_{1}\right)=n n_{1}$