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Family of Lines - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Family of Lines is considered one of the most asked concept.

  • 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

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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Family of Lines

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