Find the distance between the parallel line $15 x + 8 y - 34 = 0$ and $15 x + 8 y + 31 = 0$ .

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Solution

Comparing the given parallel lines $15 x + 8 y - 34 = 0$ and $15 x + 8 y + 31 = 0$ with the general equation of line $A x + B y + C_{1} = 0$ and $A x + B y + C_{2} = 0$ . Then,
$A = 15, B = 8, C_{1} = - 34, C_{2} = 31$

The distance between these lines is,

$d = \frac{| C_{1} - C_{2} |}{\sqrt{A^{2} + B^{2}}}$

$= \frac{| - 34 - 31 |}{\sqrt{{(15)}^{2} + {(8)}^{2}}}$

$= \frac{| - 65 |}{\sqrt{289}}$

$= \frac{65}{17} s q . u n i t s$

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Find the distance between the parallel line 15x+8y−34=0 and 15x+8y+31=0.

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