Comprehension Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the centre of hype...

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Comprehension
Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the centre of hyperbola. Tangent at any point \( P \) of hyperbola intersect the coordinate axes at \( A \) and \( B \).

Let the given line intersecrts the \( x \)-axis at \( R \). If a line through \( R \), intersect the hyperbolas at \( S \) and \( T \), then minimum value of \( R S \times R T \) is
(a) 2
(b) 4
(c) 6
(d) 8
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