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Question Number 21248 by Tinkutara last updated on 17/Sep/17

$$\mathrm{The}\mathrm{locus}\mathrm{of}\mathrm{the}\mathrm{centre}\mathrm{of}\mathrm{a}\mathrm{circle}\mathrm{which}$$$$\mathrm{touches}\mathrm{the}\mathrm{given}\mathrm{circles}\mid z-z_1\mid =$$$$\mid 3+4i\mid \mathrm{and}\mid z-z_2\mid =\mid 1+i\sqrt{3}\mid \mathrm{is}\mathrm{a}$$$$\mathrm{hyperbola},\mathrm{then}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{its}$$$$\mathrm{transverse}\mathrm{axis}\mathrm{is}$$

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