The locus of centre of circle of radius 2 units, if intercept cut on \( x \)-axis by circle is t...

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The locus of centre of circle of radius 2 units, if intercept cut on \( x \)-axis by circle is twice of intercept on \( y \)-axis is
(A) \( 4 x^{2}-3 y^{2}=4 \)
(B) \( 4 x^{2}-y^{2}=12 \)
(C) \( 4 y^{2}-x^{2}=12 \)
(D) \( 4 y^{2}-3 x^{2}=4 \)
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