(B) The distance $d$ between two parallel lines $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ is given by the formula $d = \frac{|c_1 - c_2|}{\sqrt{a^2

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(B) The distance $d$ between two parallel lines $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ is given by the formula $d = \frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}}$.Here,$a = 3$,$b = 4$,$c_1 = 7$,and $c_2 = -5$.Substituting these values into the formula:$d = \frac{|7 - (-5)|}{\sqrt{3^2 + 4^2}}$$d = \frac{|7 + 5|}{\sqrt{9 + 16}}$$d = \frac{12}{\sqrt{25}}$$d = \frac{12}{5}$.

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

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The distance between the parallel lines $3x + 4y + 7 = 0$ and $3x + 4y - 5 = 0$ is

A
$\frac{2}{5}$
B
$\frac{12}{5}$
C
$\frac{5}{12}$
D
$\frac{3}{5}$

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Straight Line

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

If the points $(1, 2)$ and $(3, 4)$ lie on opposite sides of the line $3x - 5y + a = 0$,then:

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On which side of the line $3x - 4y + 5 = 0$ does the point $(3, -4)$ lie?

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Find the set of all values of $a$ such that both the points $(1, 2)$ and $(3, 4)$ lie on the same side of the line $3x - 5y + a = 0$.

EasyAP EAMCET 2017

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The distance between the parallel lines $3x + 4y + 7 = 0$ and $3x + 4y - 5 = 0$ is

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If the points $(1, 2)$ and $(3, 4)$ lie on opposite sides of the line $3x - 5y + a = 0$,then:

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