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I have two variable {x,y} where three conditions are there

x^2 / y = 4.76*10^-11;
x / y < 4.534*10^-3;

x runs {x, 2.8*10^-11, 4.85*10^-11},

y runs {y, 2.2*10^-8, 2.5*10^-8}

I want to find the allowed region {x, y}

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  • $\begingroup$ Reduce[x^2/y == 4.76*10^-11 && x/y < 4.534*10^-3] $\endgroup$ – Feyre Aug 14 '16 at 18:49
  • $\begingroup$ Are you sure those are the functions? RegionPlot[ x/y < 4.534*10^-3, {x, 2.8*10^-11, 4.85*10^-11}, {y, 2.2*10^-8, 2.5*10^-8}] is all full. ContourPlot[ x^2/y == 4.76*10^-11, {x, 2.8*10^-11, 4.85*10^-11}, {y, 2.2*10^-8, 2.5*10^-8}] is all empty. $\endgroup$ – Feyre Aug 14 '16 at 19:24
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Reduce[x^2/y == 476*^-13 && x/y < 4534*^-6]

enter image description here

Manipulate[
 Show[
  Plot[2500000000000 x^2/119, {x, -10^-n, 0},
   PlotStyle -> Blue],
  Plot[2500000000000 x^2/119, {x, 119/11335000000, 10^-n},
   PlotStyle -> Red],
  PlotRange -> {{-10^-n, 10^-n}, Automatic}],
 {{n, 7}, Range[4, 8], ControlType -> SetterBar}]

enter image description here

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