The center of a rectangular hyperbola lies on the line \( y=2 x \). If one of the asymptotes is ...

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The center of a rectangular hyperbola lies on the line \( y=2 x \). If one of the asymptotes is \( x+y+c=0 \), then the other asymptote is:
(a) \( 6 x+3 y-4 c=0 \)
(b) \( 3 x+6 y-5 c=0 \)
(c) \( 3 x-6 y-c=0 \)
(d) \( 3 x-3 y-c=0 \)
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