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Family of Lines - Practice Questions & MCQ
Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Family of Lines is considered one of the most asked concept.
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43 Questions around this concept.
Solve by difficulty
Which of the following is NOT a conic section ?
If $a+2 b+c=0$, then the line $a x+b y+c=0$ always passes through which of the following points
The equations of the lines passing through the point (1, 0) and at a distance $\frac{\sqrt{3}}{2}$ from the origin, are
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A line passes through the point of intersection of the lines $100 x+50 y-1=0$ and $75 x+25 y+3=0$ and makes equal intercepts on the axis, its equation is
Concepts Covered - 1
Family of Lines
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 $L_1+\lambda L_2=0$ or $\mu L_1+v L_2=0$ represents a line passing through the intersection of the lines $L_1$ $=0$ and $L_2=0$ which is a fixed point. And $\lambda, \mu, v$ are constants
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