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设 为圆心（奥）（哦）(O)和两点一个一个A，乙乙B在圆圈之外。找到点碳碳C在（奥）（哦）(O)因此总和碳A + C型乙碳一个+碳乙CA + CB获取最大值和最小值并绘制通过三点的椭圆一个一个A，乙乙B，碳碳C喜欢这张照片。

我试过

Clear["Global`*"]
a = {6, 8};
b = {3, 10};
r = 5;
c = {r  Cos[t], r  Sin[t]};
mymin = NMinimize[{EuclideanDistance[a, c] + EuclideanDistance[b, c], 
    0 <= t <= 2  Pi}, t];
mymax = NMaximize[{EuclideanDistance[a, c] + EuclideanDistance[b, c], 
    0 <= t <= 2  Pi}, t];
cmax = c /. mymax[[2]];
cmin = c /. mymin[[2]];
Graphics[{Circle[{0, 0}, r], PointSize[Large], Blue, Point[a], 
  Point[b], Point[cmax], Point[cmin]}]

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最佳答案
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  • ContourPlot。
ellips = 
  ContourPlot[
   EuclideanDistance[{x, y}, a] + EuclideanDistance[{x, y}, b] == 
    EuclideanDistance[cmin,a] + EuclideanDistance[cmin,b], {x, -20, 
    20}, {y, -20, 20}];
Graphics[{Circle[{0, 0}, r], PointSize[Large], Blue, Point[a], 
  Point[b], Point[cmax], Point[cmin], ellips[[1]]}, PlotRange -> All]

  • 当我们设置a = {-1, 8};b = {5, 6};

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只是一个变体：

gs[a_, b_, rad_, rg_] := Module[{t, xp, d, r, ell, cp},
  xp = Norm[rad {Cos[t], Sin[t]} - a] + Norm[rad {Cos[t], Sin[t]} - b];
  {d, r} = Minimize[xp, t];
  ell = Norm[{x, y} - a] + Norm[{x, y} - b] == d;
  cp = rad {Cos[t], Sin[t]} /. r;
  ContourPlot[ell, {x, -rg, rg}, {y, -rg, rg}, 
   Epilog -> {Point[{{0, 0}, a, b, cp}], Text["O", {0, 0}, {-2, 0}], 
     Text["A", a, {-2, 0}], Text["B", b, {-2, 0}], 
     Text["C", cp, {-2, -2}], Circle[{0, 0}, rad]}]]

使用其他答案中的测试 a,b：

a = {6, 8};
b = {3, 10};
gs[a, b, 5, 15]
gs[{-1, 8}, {5, 6}, 5, 10]

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