Question

Find the angle between the following straight lines :

(i) y = (2 – √3)x + 5 and y = (2 + √3)x – 7

(ii) 2y – 3x + 5 = 0 and 4x + 5y + 8 = 0

(iii) x/a + y/b = 1 and x/b – y/a = 1

Answer 1

(i) y = (2 – √3)x + 5 and y = (2 + √3)x – 7

Comparing y = m₁ x + c₁
m₁ = 2 – √3
and y = (2 + √3)x – 7

Comparing y = m₂x + c₂

m₂ = 2 + √3

Angle between both lines

(ii) 2y – 3x + 5 = 0 and 4x + 5y + 8 = 0

Angle between both lines

(iii) x/a + y/b = 1 and x/b – y/a = 1

- x/a + y/b = 1 ....(i)

and x/b - y/a = 1 ....(ii)

From equation (i)

m₁ = tan θ₁ = b/a

From equation (ii)

m₂ = tan θ₂ = a/b

Therefore, angle between both lines is