Let \( \mathrm{P}(\mathrm{z}) \) be a moving point on the argand pl...

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Let \( \mathrm{P}(\mathrm{z}) \) be a moving point on the argand plane satisfying || \( \mathrm{z}+4|-| \mathrm{z}-4||=4 \) where \( \mathrm{z}=\mathrm{x}+ \) iy, then locus of \( \mathrm{P}(\mathrm{z}) \) is a hyperbola whose
(A) distance between foci equals 4
\( \mathrm{P} \)
(B) eccentricity equals 2
(C) distance between directrices equals 2
(D) product of the length of perpendiculars from foci upon any tangent equals 4
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