Q. 11

# The slope of a line is double of the slope of another line. If tangent of the angle between them is find the slopes of the lines.

Let the slopes of the two given lines be m and 2m and θ be the angle between them

The according to questions

tan θ =

Now tan θ =

or = or =

or 1 + 2m2 = 3m

or 2m2 - 2m + 1= 0

or 2m2 - 2m -m + 1= 0

or 2m(m – 1) – 1(m – 1) = 0

or (m – 1) (2m – 1) = 0

or m = 1, m =

Hence, the slopes of the lines are

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