pp=ImplicitRegion[Sum[EuclideanDistance[{x,y},pt],{pt,CirclePoints[{0,0.75},
{5,0Degree},4]}]==24 &&(-1+0.04 x^2+0.8 y^2)^3==0.00032 x^2 y^3,{x,y}]
Reduce[Element[{x,y},pp],{x,y}]//LogicalExpand
I use above method to find the intersection point value,but 2 hours past, there's no any result.
Then I plot:
a=ContourPlot[(-1+0.04 x^2+0.8 y^2)^3==0.00032 x^2 y^3,{x,-6,6},{y,-6,6}];
b=ContourPlot[Sum[EuclideanDistance[{x,y},pt],{pt,CirclePoints[{0,0.75},
{5,0Degree},4]}]==24,{x,-6,6},{y,-6,6}];
Show[a,b]
It's easy to find there are intersection points.
How to calculate the intersection points value?
0.04
and0.8
, and your use ofEuclideanDistance[]
, which introduces anAbs[]
that gives solvers trouble. $\endgroup$solvers trouble
notice. $\endgroup$0.123456
. So if you want numerical values, then your problem can be easily solved. But if you actually want something exact, then you need to solve for the roots of a high-degree polynomial which takes a very long time (and might not even be possible). $\endgroup$