Question

the angle between the lines x-2y =y and y- 2x =5 is ​

Answer 1

Given:

The angle between the linez x- 2y =y and y- 2x =5 is

Solution:

Angle between the lines,

⇒ x - 2y = 2.

⇒ y - 2x = 5.

As we know that,

Slope of the line : y = mx + c.

Equation : x - 2y = 2.

⇒ x = 2 + 2y.

⇒ x - 2 = 2y.

⇒ x/2 - 2/2 = y.

Slope = M₁ = 1/2.

Equation : y - 2x = 5.

⇒ y = 5 + 2x.

Slope = M₂ = 2.

As we know that,

Formula of angle between the lines,

⇒ tan∅ = | m₁ - m₂/1 + m₁m₂|

⇒ tan∅ = | 1/2 - 2/1 + (1/2)(2) |.

⇒ tan∅ = | 1 - 4/2/1 + 1 |.

⇒ tan∅ = | -3/2/2 |.

⇒ tan∅ = | -3/4 |.

⇒ tan∅ = 3/4.

⇒ ∅ = tan⁻¹(3/4).