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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 40 of 74
Marks: +1, -0
Find the distance between parallel lines
(i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0
(ii) l(x + y) + p = 0 and l(x + y) – r = 0.
Solution:  
If lines are Ax + By + C1C_1 = 0 and Ax + By + C2C_2 = 0, then distance between parallel lines, d = C1C2A2+B2\frac{\left|C_1-C_2\right|}{\sqrt{A^2+B^2}}
(i) Here, A = 15, B = 8, C1C_1 = – 34, C2C_2 = 31
d = 3431(15)2+(8)2\frac{\left|-34-31\right|}{\sqrt{(15)^2+(8)^2}} = 6517\frac{65}{17} units
(ii) The line can be re-written as lx + ly + p = 0 and lx + ly – r = 0
Here A = l, B = l, C1C_1 = p, C2C_2 = –r
d = p+r(l)2+(l)2\frac{\left|p+r\right|}{\sqrt{(l)^2+(l)^2}} = p+rl2\frac{p+r}{l\sqrt{2}} units
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