A median of a triangle through mid-point of $(-c,0),(c,0) $ is such so that ratio of cosines of angles between sides/median

$$ \cos \phi/\cos \psi =e $$ is a constant. Is the curve known?

$$ \frac {((x + c) x + y^2)}{((x - c) x + y^2)} \, \sqrt{ \frac{((x - c) ^2 + y^2}{((x + c) ^2 + y^2}} = e $$

 Apollonius Circle Types

Seems to be a fourth order curve:

  • $\begingroup$ It doesn't appear as a known curve. It can somewhat be considered as a "generalized conic" : see the article (en.wikipedia.org/wiki/Generalized_conic) $\endgroup$ – Jean Marie Aug 25 '16 at 8:55
  • $\begingroup$ Thanks. Actually I was playing with variants of the Apollonius Circle .. no luck in its generalization.. $\endgroup$ – Narasimham Aug 25 '16 at 9:25
  • $\begingroup$ The curve is symmetriic wrt x- and y- axes. $\endgroup$ – Narasimham Aug 27 '16 at 8:23

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