Given that the straight lines (kx – 5y + 6 = 0) and (mx + ny – 1 = 0) are parallel, find a relationship connecting the constants m, n and k.
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A.
5n – km = 0 -
B.
kn + 5m = 0 -
C.
5n + km = 0 -
D.
kn – 5m = 0
Correct Answer: Option B
Explanation
Two lines are parallel if and only if their slopes are equal.
(kx – 5y + 6 = 0 implies 5y = kx + 6)
(y = frac{k}{5}x + frac{6}{5})
(Slope = frac{k}{5})
(mx + ny – 1 = 0 implies ny = 1 – mx)
(y = frac{1}{n} – frac{m}{n}x)
(Slope = -frac{m}{n})
(Parallel implies frac{k}{5} = -frac{m}{n})
(-5m = kn implies 5m + kn = 0)