Equation of Parallel and Perpendicular Lines to a Given Line
Category : JEE Main & Advanced
(1) Equation of a line which is parallel to \[ax+by+c=0\] is \[ax+by+\lambda =0\].
(2) Equation of a line which is perpendicular to \[ax+by+c=0\] is \[bx-ay+\lambda =0\].
The value of \[\lambda \] in both cases is obtained with the help of additional information given in the problem.
(3) If the equation of line be \[a\sin \theta +b\cos \theta =c\], then line
(i) Parallel to it, \[a\sin \theta +b\cos \theta =d\]
(ii) Perpendicular to it, \[a\sin \left( \frac{\pi }{2}+\theta \right)+b\cos \left( \frac{\pi }{2}+\theta \right)=d\].
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