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प्रश्न
Find the distance between parallel lines l (x + y) + p = 0 and l (x + y) – r = 0
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उत्तर
It is known that the distance (d) between parallel lines Ax + By + C1 = 0 and Ax + By + C2 = 0 is
given by d = `(|C_1 - C_2|)/sqrt(A^2 + B^2)`
The given parallel lines are l (x + y) + p = 0 and l (x + y) – r = 0.
lx + ly + p = 0 and lx + ly – r = 0
Here, A = l, B = l, C1 = p, and C2 = –r.
Therefore, the distance between the parallel lines is
`d = (|C_1 - C_2|)/sqrt(A^2 + B^2)` = `(|p + r|)/sqrt(l^2 + l^2)` units
= `(|p + r|)/sqrt(2l^2)` units
= `(|p + r|)/(lsqrt2)` units
= `1/sqrt2|(p + r)/(l)|` units
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