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Question Number 94081 by Rio Michael last updated on 16/May/20

$$P\mathrm{is}\mathrm{the}\mathrm{point}\mathrm{representing}\mathrm{the}\mathrm{complex}\mathrm{number}$$$$z=r(\cos \theta +i\sin \theta )\mathrm{in}\mathrm{an}\mathrm{argand}\mathrm{diagram}\mathrm{such}$$$$\mathrm{that}\mid z-a\mid \mid z+a\mid =a^2.\mathrm{Show}\mathrm{that}P\mathrm{moves}\mathrm{on}\mathrm{the}\mathrm{curve}$$$$\mathrm{whose}\mathrm{equation}\mathrm{is}{r}^2=2a^2\cos 2\theta .\mathrm{sketch}\mathrm{the}\mathrm{curve}$$$$r^2=2a^2\cos 2\theta ,\mathrm{showing}\mathrm{clearly}\mathrm{the}\mathrm{tangents}\mathrm{at}\mathrm{the}\mathrm{pole}.$$

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