If \( y=m_{1} x+c_{1} \) and \( y=m_{2} x+c_{2}, m_{1} \neq m_{2} \) are two common tangents of ...

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If \( y=m_{1} x+c_{1} \) and \( y=m_{2} x+c_{2}, m_{1} \neq m_{2} \) are two common tangents of circle \( x^{2}+y^{2}=2 \) and parabola \( y^{2}=x \), then the value of \( 8\left|m_{1} m_{2}\right| \) is equal to
(a) \( 3+4 \sqrt{2} \)
(b) \( -5+6 \sqrt{2} \)
(c) \( -4+3 \sqrt{2} \)
(d) \( 7+6 \sqrt{2} \)
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