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Question

If the straight line xcosθ+ysinθ=2 touches the circle x2+y22x=0 then

A
θ=nπ,nZ
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B
θ=(2n+1)π,nZ
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C
θ=2nπ,nZ
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D
θ=(2n+1)π2,nZ
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Solution

The correct option is C θ=2nπ,nZ
x2+y22x=0
Centre (1,0) and radius =1

If the line touches the circle, then
∣ ∣1cosθ2sin2θ+cos2θ∣ ∣=1

cosθ=3 or cosθ=1
θ=2nπ,nZ

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