    Question

# If θ1 and θ2 be the angles which the lines (x2+y2)(cos2 θ sin2 α+sin2θ)=(x tan α−y sin θ)2 make with the axis of x, then if θ=π6, tan θ1+tan θ2 is equal to

A
(83)sin2 α
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B
(83)cosec 2α
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C
83 cosec 2α
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D
4 cosec 2α
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Solution

## The correct option is B (−83)cosec 2αThe given equation can be written as (x2+y2)(cos2 θ sin2 α+sin2 θ)=x2 tan2 α−2xy tan α sin θ+y2 sin2 θ or (cos2 θ sin2 α+sin2 θ−tan2 α)x2+2(tan α sin θ)xy+cos2 θ sin2 αy2=0 Since the slope of these lines are given as tanθ1 and tan θ2. and sum of the slopes =−2 tan α sin θcos2 θ sin2 α ⇒ tan θ1+tan θ2=−2 tan α2×(34)×sin2 α (∵ θ=π6)=−(83)cosec 2α  Suggest Corrections  0      Similar questions  Related Videos   Basic Concepts
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