# Family of Straight Lines

Let

*L*_{1}â‰¡*a*_{1}*x*+*b*_{1}*y*+*c*_{1}= 0 and*L*_{2}â‰¡*a*_{1}*x*+*b*_{1}*y*+*c*_{1}= 0. Then general equation of any straight line passing through the point of intersection of*L*_{1}and*L*_{2}is given by*L*_{1}+*Î»L*_{2}= 0, where*Î»*âˆˆ*R*.These lines form a family of straight lines. Also this general equation satisfies point of intersection of

*L*_{1}and*L*_{2}for any value of*Î»*.

*Notes:*- Variable straight line
*ax*+*by*+*c*= 0, where*a*,*b*,*c*are real form of a family of straight line as for different values of*a*,*b*,*c*they are related by any linear relation, like*al*+*bm*+*cn*= 0, where*l*,*m*,*n*are constants.*ax*+*by*= 0*a*and*b.* - If a straight line is such that the algebraic sum of the perpendiculars drawn upon it from any number of fixed points is zero; then line always passes through a fixed point.