Question

Find the distance between parallel lines y=mx +c, y=mx +d

Answer 1

We know that slopes of two parallel lines are equal. Therefore, two parallel lines can be taken in the form

y = mx + c1 … (1)

and y = mx + c2 … (2)

Line (1) will intersect x-axis at the point A (–c1/m, 0) as shown in figure.

Distance between two lines is equal to the length of the perpendicular from point A to line (2). Therefore, distance between the lines (1) and (2) is

|(–m)(–c1/m) + (–c2)|/√(1 + m2) or d = |c1–c2|/√(1+m2).

Thus the distance d between two parallel liens y = mx + c1 and y = mx + c2 is given by d = |C1–C2|/√A2 + B2.

Answer 2

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