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…

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
  1. $r^2\left(I_1+m m_1\right)=n n_1$
  2. $r^2\left(I_1-m m_1\right)=n n_1$
  3. $r^2\left(I_1+m m_1\right)+n n_1=0$
  4. $r^2\left(I m_1+I_1 m\right)=n n_1$

Solution

Condition for conjugate line is $ r^2\left(I_1+m m_1\right)=n n_1 $

Asked in: AP EAMCET 2014

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