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If two ellipses are intersecting at a point,is it necessary that the line drawn joining the centre of those two ellipses should also pass through the point of intersection (of ellipse)? (if yes,how to prove it ?!)

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    $\begingroup$ That's not even true for circles! $\endgroup$ – Henning Makholm May 23 '16 at 14:14
  • $\begingroup$ But this is true if the two circles intersect at a single point ; this is probably what the OP means. $\endgroup$ – paf May 23 '16 at 14:24
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If by "intersecting at point" you mean external tangency then the answer to your question is "No". You can refer to the first diagram on this link below See a diagrammatic example

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