The locus of the centre of a circle which touches the given circles |z−z1|=|3+4i|and|z−z2|=|1+i3| is a hyperbola ,then the length of its transverse axis is

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The locus of the centre of a circle which touches the given circles $| z - z_{1} | = | 3 + 4 i | a n d | z - z_{2} | = | 1 + i \sqrt{3} |$ is a hyperbola ,then the length of its transverse axis is

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answer is 3.

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Detailed Solution

$| z - z_{1} | = r + 5 | z - z_{2} | = r + 2 | Z - Z_{1} | - | Z - Z_{2} | = 3$
locus is hyper bola and we know
$P F_{1} - P F_{2} = 2 a$ =Length of transverse axis =3

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