(B) The given lines are $3x - 2y - 1 = 0$ and $6x - 4y + 9 = 0$. To make the coefficients of $x$ and $y$ same,multiply the first equation by $2$: $6x

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(B) The given lines are $3x - 2y - 1 = 0$ and $6x - 4y + 9 = 0$. To make the coefficients of $x$ and $y$ same,multiply the first equation by $2$: $6x - 4y - 2 = 0$. The distance $d$ between two parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$ is given by $d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$. Here,$A = 6, B = -4, C_1 = -2, C_2 = 9$. $d = \frac{|-2 - 9|}{\sqrt{6^2 + (-4)^2}} = \frac{|-11|}{\sqrt{36 + 16}} = \frac{11}{\sqrt{52}}$.

Class 11 Mathematics Straight Lines Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

Easy

The distance between the lines $3x - 2y = 1$ and $6x - 4y + 9 = 0$ is

A
$\frac{1}{\sqrt{52}}$
B
$\frac{11}{\sqrt{52}}$
C
$\frac{4}{\sqrt{13}}$
D
$\frac{6}{\sqrt{13}}$

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Straight Lines

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Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

Find the distance of the point $(3, -5)$ from the line $3x - 4y - 26 = 0$.

Easy

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If a line $l$ passes through $(k, 2k), (3k, 3k)$ and $(3, 1)$,where $k \neq 0$,then the distance from the origin to the line $l$ is

EasyAP EAMCET 2014

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Find the length of the perpendicular drawn from the origin to the line $\sqrt{3}x - y + 2 = 0$.

Easy

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Let two points be $A(1, -1)$ and $B(0, 2)$. If a point $P(x', y')$ is such that the area of $\Delta PAB = 5 \; \text{sq units}$ and it lies on the line $3x + y - 4\lambda = 0$,then a value of $\lambda$ is

DifficultJEE MAIN 2020

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The distance between the lines $3x - 2y = 1$ and $6x - 4y + 9 = 0$ is

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