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The locus of the point of intersection of the lines $x \sin θ + (1 - \cos θ) y = a \sin θ$ and $x \sin θ - (1 + \cos θ) y + a \sin θ = 0$ is

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x2-y2=a2

x2+y2=a2

y2=ax

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Correct option is B

From the given equations we have1−cos⁡θsin⁡θ=a−xy and 1+cos⁡θsin⁡θ=a+xyMultiplying we get 1−cos2⁡θsin2⁡θ=a2−x2y2 ⇒ x2+y2=a2

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The locus of the point of intersection of the lines x sinθ+(1-cosθ)y=asinθ and xsinθ-(1+cosθ)y+asinθ=0 is

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The locus of the point of intersection of the lines $x \sin θ + (1 - \cos θ) y = a \sin θ$ and $x \sin θ - (1 + \cos θ) y + a \sin θ = 0$ is