# Is this curve known?

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?

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

Seems to be a fourth order curve:

• 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) – Jean Marie Aug 25 '16 at 8:55
• Thanks. Actually I was playing with variants of the Apollonius Circle .. no luck in its generalization.. – Narasimham Aug 25 '16 at 9:25
• The curve is symmetriic wrt x- and y- axes. – Narasimham Aug 27 '16 at 8:23