The value of \( m \) for which the line \( y=m x+2 \) becomes a tangent to the hyperbola \( 4 x^...

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The value of \( m \) for which the line \( y=m x+2 \) becomes a tangent to the hyperbola \( 4 x^{2}-9 y^{2}=36 \) is
(A) \( \pm \frac{2}{3} \)
(B) \( \pm \frac{2 \sqrt{2}}{3} \)
(C) \( \pm \frac{8}{9} \)
(D) \( \pm \frac{4 \sqrt{2}}{3} \)
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