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The distance between the parallel lines 4x + 3y = 12 and 4x + 3y = 17 is

(A) 1

(B) 5

(C) 29

(D) none of these

1 Answer

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by (46.8k points)
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Best answer

Correct option is (A) 1

The given lines are

\(4x + 3y -12 = 0\)

\(4x + 3y -17 = 0\)

As we know that distance between the parallel lines (d) is given as-

\(d = \frac{|c_2 - c_1|}{\sqrt{a^2 + b^2}}\)

Therefore,

\(d = \frac{|-17 -(- 12)|}{\sqrt{4^2 + 3^2}}\)

\(= \frac {|-17 + 12|}{\sqrt{1 6 + 9}}\)

\(= \frac {|-5|}{\sqrt{25}}\)

\(= \frac {5}{5}\)

\(= 1\)

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