The Evans conic is the conic section passing through the Fermat points 
and 
,
the inner and outer Napoleon points 
and 
,
and the isodynamic points 
and 
of a triangle. It has trilinear equation
![a^2alpha^2(-3S^2+S_A^2)(-S^2+3S_A^2)(S_B-S_C)^2+2bcbetagamma(S_A-S_B)(-S_A+S_C)[3a^4S_A^2+(a^2S_A+S_BS_C)(S_B^2-6S_BS_C+SS_C^2)]+[cyclic trilinears],](/images/equations/EvansConic/NumberedEquation1.svg) |
where 
, 
, 
,
and 
is Conway
triangle notation (P. Moses, pers. comm., Jan. 12, 2005).
The center of the Evans conic has center function
 |
where 
is the area of the reference triangle and 
is the Brocard
angle (P. Moses, pers. comm., Jan. 12, 2005), which is Kimberling
center 
.
The Evans conic passes through Kimberling centers 
for 
(first Fermat point),
14 (second Fermat point), 15 (first
isodynamic point), 16 (second isodynamic
point), 17 (first Napoleon point), 18
(second Napoleon point), 590, and 615.
