find the angle between x+2y+9=0 and 3x+y+7=0
Answers
EXPLANATION.
Angle between the lines,
⇒ x + 2y + 9 = 0.
⇒ 3x + y + 7 = 0.
As we know that,
Slope of intercept = y = mx + c.
⇒ x + 2y + 9 = 0.
⇒ 2y = - x - 9.
⇒ y = - x/2 - 9/2.
Slope of the line x + 2y + 9 = 0 is -1/2.
M₁ = -1/2.
⇒ 3x + y + 7 = 0.
⇒ y = - 3x - 7.
Slope of the line 3x + y + 7 = 0 is = -3.
⇒ M₂ = -3.
As we know that,
⇒ tan∅ = | M₁ - M₂/1 + M₁M₂ |.
Put the value of M₁ & M₂ in equation, we get.
⇒ tan∅ = | -1/2 - (-3)/1 + (-1/2)(-3) |.
⇒ tan∅ = | -1/2 + 3/1 + 3/2 |.
⇒ tan∅ = | - 1 + 6/2 + 3/2 |.
⇒ tan∅ = | 5/2/5/2 |.
⇒ tan∅ = 1.
⇒ tan∅ = 45°.
∅ = π/4.
MORE INFORMATION.
Equation of tangent.
Equation of tangent to the curve y = f(x) at p(x₁, y₁) is,
(y - y₁) = (dy/dx) (x - x₁).
(1) = The tangent at (x₁, y₁) is parallel to x-axis = (dy/dx) = 0.
(2) = The tangent at (x₁, y₁) is parallel to y-axis = (dy/dx) = ∞.
(3) = The tangent lines makes equal angle with the axes = (dy/dx) = ± 1.