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$\begingroup$ Why my same method with you,but give a wrong result?Clear["*"];re=ImplicitRegion[((1.2 x)^2+(1.4 y)^2-1)^3-(1.3 x)^2 y^3==0,{x,y}];soln=ArgMax[{EuclideanDistance[{x1,y1},{x2,y2}],{{x1,y1}[Element]re,{x2,y2}[Element]re}},{x1,y1,x2,y2}]; ContourPlot[((1.2 x)^2+(1.4 y)^2-1)^3-(1.3 x)^2 y^3==0,{x,-1.5,1.5},{y,-3/2,3/2},AspectRatio->Automatic,Epilog->{PointSize[Large],Red,Point[{{soln[[1]],soln[[2]]},{soln[[3]],soln[[4]]}}]}]` $\endgroup$

yode
– yode

2016-03-29 09:11:12 +00:00
Commented Mar 29, 2016 at 9:11
$\begingroup$ @yode I don't know why it fails, maybe a bug? $\endgroup$

RunnyKine
– RunnyKine

2016-03-29 09:41:22 +00:00
Commented Mar 29, 2016 at 9:41
$\begingroup$ I think so.Thanks for your confirmation. $\endgroup$

yode
– yode

2016-03-29 09:59:23 +00:00
Commented Mar 29, 2016 at 9:59

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