Find the distance between the parallel lines 3x + 4y + 7 = 0 and 3x + 4y - 5 = 0 from the origin.

Distance d between two parallel lines y = mx + c1 and y = mx + c2 is given by
d = |C1–C2|/√A2 + B2

d1= distance of perpendicular from (0,0) to 3x+4y+7 = 0

Using formula, we get

d1= (3 × 0 + 4 × 0 + 7) /√(32+42) = 7/5

d2 = (3 × 0 + 4 × 0 + (−5) )/ √(32+42) = −5/5

Required distance is =|d1 − d2| = ∣7/5 − (−5/5)∣ = 12/5

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