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 m₁ and m be the slope of the two given lines such that m₁= 2m

We know that if θ is the angle between the lines l1 and l2 with slope m₁ and m₂, then

Given here that the tangent of the angle between the two lines is

∴

⇒

Case 1

⇒

⇒ 1+2m² = -3m

⇒ 2m² +1 +3m = 0

⇒2m(m+1) + 1(m+1)=0

⇒(2m+1)(m+1)= 0

⇒ m =-1 or

If m = -1, then the slope of the lines are -1 and -2

If m = , then the slope of the lines are and -1

Case 2

⇒

⇒ 2m² +1 -3m = 0

⇒ m = 1 or 1/2

If m = 1, then the slope of the lines are 1 and 2

If m = , then the slope of the lines are and 1

Hence the slope of the lines are -1 and -2 or and -1 or 1 and 2 or and 1.