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Find the distance between parallel lines \[\] $15x+8y-34=0$ and $ 15x+8y+31=0$

$\begin{array}{1 1}(A)\;\large\frac{-65}{17}\: units \\(B)\; \large\frac{65}{17}\: units \\(C)\; \large\frac{|65|}{17}\: units \\(D)\;\text{None of the above} \end{array} $

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  • Distance between parallel lines is $d=\large\frac{|c_1-c_2|}{\sqrt{A^2+B^2}}$
The given parallel lines are $15x+8y-34=0$ and $15x+8y+31=0$
Here $A = 15, B =8 , C_1=-34\: and \: C_2=31$
Substituting the values we get,
$d = \large\frac{|-34-31|}{\sqrt{15^2+8^2}}$$= \large\frac{|-65|}{17}$
$ = \large\frac{65}{17}$ units.
answered May 9, 2014 by thanvigandhi_1

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