Question

# The equation of the straight line through the origin making angle ϕ with the line y=mx+b, isy=(m+tanϕ1−mtanϕ)xy=(m−tanϕ1+tanϕ)xy=(tanϕ1+mtanϕ)xy=(m−tanϕ1+mtanϕ)x

Solution

## The correct options are A y=(m+tanϕ1−mtanϕ)x D y=(m−tanϕ1+mtanϕ)xSince, 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±tanϕ1∓mtanϕ So, equation of required line will be y=(m±tanϕ1∓mtanϕ)x

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