Find the tangent of the following lines with +ve x-axis.(i) √3x –

1.	Find the tangent of the following lines with +ve x-axis.(i) √3x – y + 2 = 0(ii) x + √3y – 2√3 = 0
Answer» (i) √3x – y + 2 = 0 ⇒ y = √3x + 2 Comparing with y = mx + c m = √3 ⇒ m = tan θ tan θ = √3 = tan 60° Thus tangent of required angle is 60°. (ii) x + √3y – 2√3 = 0 ⇒ √3y = - x + 2√3 ⇒ y = (- 1/√3)x + 2 Comparing with y = mx + c m = tanθ = - 1/√3 ⇒ tanθ = tan150° Thus, tangent of required angle is 150°.

Find the tangent of the following lines with +ve x-axis.(i) √3x – y + 2 = 0(ii) x + √3y – 2√3 = 0

Answer»

(i) √3x – y + 2 = 0

⇒ y = √3x + 2

Comparing with y = mx + c

m = √3

⇒ m = tan θ

tan θ = √3 = tan 60°

Thus tangent of required angle is 60°.

(ii) x + √3y – 2√3 = 0

⇒ √3y = - x + 2√3

⇒ y = (- 1/√3)x + 2

Comparing with y = mx + c

m = tanθ = - 1/√3

⇒ tanθ = tan150°

Thus, tangent of required angle is 150°.