Family of Lines - Practice Questions & MCQ

Family of Lines

Any equation of line through the point of intersection of the lines $L_1=a_1 x+b_1 y+c_1=0$ and $L_2=a_2 x+b_2 y+c_2=0$ can be represented as

$
\begin{aligned}
& \mathrm{a}_1 \mathrm{x}+\mathrm{b}_1 \mathrm{y}+\mathrm{c}_1+\lambda\left(\mathrm{a}_2 \mathrm{x}+\mathrm{b}_2 \mathrm{y}+\mathrm{c}_2\right)=0 \\
& \text { or, } \mathrm{L}_1+\lambda \mathrm{L}_2=0
\end{aligned}
$

Where $\lambda$ is a parameter.

Note:.

• The equation L₁ + λL₂ = 0 or μL₁ + νL₂ = 0  represents a line passing through the intersection of the lines L₁ = 0 and L₂ = 0 which is a fixed point. And λ,  μ , ν are constants.