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  • Find the distance between parallel lines. (ii) l (x + y) + p = 0 and l (x + y) – r = 0.

Q : 6     Find the distance between parallel lines

            (ii)  l(x+y)+p=0 and l(x+y)-r = 0

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Given equations of lines are
l(x+y)+p=0 and l(x+y)-r = 0
it is given that these lines are parallel
Therefore,
d = \frac{ |C_2-C_1|}{\sqrt{A^2+B^2}}
A = l , B = l , C_1= -r \ and \ C_2 = p
Now,
d = \frac{|p-(-r)|}{\sqrt{l^2+l^2}}= \frac{|p+r|}{\sqrt{2l^2}}= \frac{|p+r|}{\sqrt{2}|l|}
Therefore, the distance between two lines is \frac{1}{\sqrt2}\left | \frac{p+r}{l} \right |

Posted by

Gautam harsolia

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