Question

Prove that following straight lines are parallel

(i) 2y = mx + c and 4y = 2mx

(ii) x cos α + y sin α = p and x + y tan α = 5 tan α

Answer 1

(i) 2y = mx + c

⇒ y = mx/2 + c/2

⇒ y = (m/2)x + c/2 ....(i)

Comparing with y = m₁x + c₁
m₁ = m/2
4y = 2 mx

Thus, both lines will be parallel.

(ii) x cos α + y sin α = p

⇒ y sin α = – x cos α + p

We see that

m₁ = m₂ = – cot α

Therefore both line will be parallel.