Tangents are drawn to a unit circle with centre at the origin from each point on the line \( 2 \...

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Tangents are drawn to a unit circle with centre at the origin from each point on the line \( 2 \mathrm{x}+\mathrm{y}=4 \).
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Then the equation to the locus of the middle point of the chord of contact is -
(A) \( 2\left(x^{2}+y^{2}\right)=x+y \)
(B) \( 2\left(x^{2}+y^{2}\right)=x+2 y \)
(C) \( 4\left(x^{2}+y^{2}\right)=2 x+y \)
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