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Question

The equation of the straight line through the origin making angle ϕ with the line y=mx+b, is
  1. y=(m+tanϕ1mtanϕ)x
  2. y=(mtanϕ1+tanϕ)x
  3. y=(tanϕ1+mtanϕ)x
  4. y=(mtanϕ1+mtanϕ)x


Solution

The correct options are
A y=(m+tanϕ1mtanϕ)x
D y=(mtanϕ1+mtanϕ)x
Since, required line makes an angle of ϕ with y=mx+b
Let m=tanθ
Hence, the required line makes θ±ϕ angle with x axis.

Now, 
tan(θ±ϕ)=m±tanϕ1mtanϕ

So, equation of required line will be
y=(m±tanϕ1mtanϕ)x

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