Find the angle between the line x-2y+1=0 & 2x+6y-5=0
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EXPLANATION.
Angle between the line.
⇒ x - 2y + 1 = 0. - - - - - (1).
⇒ 2x + 6y - 5 = 0. - - - - - (2).
As we know that,
Slope of line = -a/b.
Slope of the line : x - 2y + 1 = 0.
⇒ M₁ = -(1)/-2 = 1/2.
Slope of the line : 2x + 6y - 5 = 0.
⇒ M₂ = -(2)/6 = -1/3.
As we know that,
⇒ tanθ = |m₁ - m₂/1 + m₁m₂|.
⇒ tanθ = |1/2 - (-1/3)/1 + (1/2)(-1/3)|.
⇒ tanθ = |1/2 + 1/3/1 - 1/6|.
⇒ tanθ = |3 + 2/6/6 - 1/6|.
⇒ tanθ = |5/6/5/6|.
⇒ tanθ = | 5/6 x 6/5 |.
⇒ tanθ = |1|.
⇒ tanθ = tan45°
⇒ θ = 45° = π/4.
MORE INFORMATION.
The angle between two straight lines.
(1) = tanθ = |m₁ - m₂/1 + m₁m₂|.
(2) = Two lines are parallel if : m₁ = m₂.
(3) = Two lines are perpendicular if : m₁m₂ = - 1.
(4) = Two lines a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are coincident only and only if, a₁/a₂ = b₁/b₂ = c₁/c₂.
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