The slope of a line L is 2 . If m 1 , m 2 are slopes of two lines which are inclined at an angle of π 6 with L , then m 1 + m 2 =

Question

The slope of a line L is 2 . If m 1 , m 2 are slopes of two lines which are inclined at an angle of π 6 with L , then m 1 + m 2 =, - 11, 16, 11, - 16

MARKS App · Accepted Answer

Angle between two lines, tan θ = m - m ' 1 + m m ' ⇒ tan π 6 = m - 2 1 + 2 m 2 Squaring both the sides ⇒ 4 m 2 + 4 m + 1 1 3 = m 2 - 4 m + 4 ⇒ 4 m 2 + 4 m + 1 = 3 m 2 - 12 m + 12 ⇒ m 2 + 16 m - 11 = 0 , where roots are m 1 & m 2 So, = m 1 + m 2 = - 16 1 = - 16

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