Find the distance between the parallel lines | vedclass

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(A) 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^

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$\frac{1}{\sqrt{2}} \frac{|p+r|}{l}$

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(A) The distance $(d)$ between two parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$ is given by the formula $d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$.The given equations are $l(x + y) + p = 0$ and $l(x + y) - r = 0$.Expanding these,we get $lx + ly + p = 0$ and $lx + ly - r = 0$.Here,$A = l$,$B = l$,$C_1 = p$,and $C_2 = -r$.Substituting these values into the formula:$d = \frac{|p - (-r)|}{\sqrt{l^2 + l^2}}$$d = \frac{|p + r|}{\sqrt{2l^2}}$$d = \frac{|p + r|}{l\sqrt{2}}$$d = \frac{1}{\sqrt{2}} \frac{|p + r|}{l}$ units.

Find the distance between the parallel lines $l(x + y) + p = 0$ and $l(x + y) - r = 0$.

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