# How can I find the boundary function in RegionPlot?

Posted 9 years ago
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 HelloI have a problem with finding the function that gives the boundary curve in RegionPlot command. I use the following code to make the regions RegionPlot[{{x^3 - y^2 > 2 y && x^2 + y^3 > 2 x }, {x^3 - y^2 < 2 y && x^2 + y^3 > 2 x }}, {x, -1, 1}, {y, -1, .1}, PlotStyle -> {Green, Yellow}, BoundaryStyle -> {Black, Thick}]Here we see a black thick curve between the green and yellow regions, I mean the boundary that separates the black and green regions (I showed it with a red arrow).Now, how can I find its equation or at least the list of points living on this curve?Best Hadi Attachments:
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Posted 9 years ago
 Both regions have x^2 + y^3 > 2 x but the first has x^3 - y^2 > 2 y and the second has x^3 - y^2 < 2 y, so I would expect the boundary to be x^2 + y^3 == 2 x where x^2 + y^3 > 2 x. You can check this withContourPlot[x^3 - y^2 == 2 y, {x, -1, 1}, {y, -1, 1}, RegionFunction -> Function[{x, y}, x^2 + y^3 > 2 x] ]
Posted 9 years ago
 It is just one of your inequalities but with an = ContourPlot[x^3 - y^2 == 2 y, {x, -1, 1}, {y, -1, .1}]