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How do I plot something like $$\{(x,y): 1 \leq x^2 + y^2 < 9\}?$$

I want to be able to make the boundary $x^2 + y^2 = 9$ dotted line and the unit circle filled and coloured region in between? I tried using

RegionPlot[1 <= x^2 + y^2 < 9, {x, -3.5, 3.5}, {y, -3.5, 3.5}, 
  Frame -> False, AxesOrigin -> {0, 0}, Axes -> True]

But that gave me a bolded boundary on $x^2 + y^2 = 9$

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All you're missing is the option for BoundaryStyle

RegionPlot[1 <= x^2 + y^2 < 9, {x, -3.5, 3.5}, {y, -3.5, 3.5}, 
 Frame -> False, AxesOrigin -> {0, 0}, Axes -> True, 
 BoundaryStyle -> {Dotted, Thickness[0.005]}]

enter image description here

If you want the unit circle filled, you can RegionPlot that separately:

Show[RegionPlot[1 <= x^2 + y^2 < 9, {x, -3.5, 3.5}, {y, -3.5, 3.5}, 
  Frame -> False, AxesOrigin -> {0, 0}, Axes -> True, 
  BoundaryStyle -> {Dotted, Thickness[0.005]}], 
 RegionPlot[x^2 + y^2 < 1, {x, -3.5, 3.5}, {y, -3.5, 3.5}, 
  PlotStyle -> Red, BoundaryStyle -> {Dotted, Thickness[0.005]}]]

You can find all these (and more) in the help for RegionPlot.

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  • $\begingroup$ Your second code gives me a red filled unit circle. $\endgroup$
    – Hawk
    Jan 24 '14 at 2:40
  • $\begingroup$ Nvm I got it fixed. thanks $\endgroup$
    – Hawk
    Jan 24 '14 at 2:47
  • $\begingroup$ You did say "and the unit circle filled" so I filled the unit circle with Red... or not... $\endgroup$
    – bill s
    Jan 24 '14 at 3:26
  • $\begingroup$ No that would be the unit disk. $\endgroup$
    – Hawk
    Jan 25 '14 at 2:22

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