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Find the distance between parallel lines (i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0.

Q : 6      Find the distance between parallel lines

             (i) 15x+8y-34=0  and  15x+8y+31=0.

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Given equations of lines are
 15x+8y-34=0  and  15x+8y+31=0
it is given that these lines are parallel
Therefore,
d = \frac{ |C_2-C_1|}{\sqrt{A^2+B^2}}
A = 15 , B = 8 , C_1= -34 \ and \ C_2 = 31
Now,
d = \frac{|31-(-34)|}{\sqrt{15^2+8^2}}= \frac{|31+34|}{\sqrt{225+64}}= \frac{|65|}{\sqrt{289}} = \frac{65}{17}
Therefore, the distance between two lines is \frac{65}{17} \ units
 

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