If the values of \( m \) for which the line \( y=m x+2 \sqrt{5} \) touches the hyperbola \( 16 x...

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If the values of \( m \) for which the line \( y=m x+2 \sqrt{5} \) touches the hyperbola \( 16 x^{2}-9 y^{2}=144 \) are the roots of the equation \( x^{2} \) \( -(a+b) x-4=0 \), then the value of \( (a+b) \) is equal to:
(a) 2
(b) 4
(c) Zero
(d) 8
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