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how can I plot the below green curve? Is there any way I could manipulate the step sizes?

enter image description here

This is my current code:

s1 = Plot[{Table[1/2 (c - Sqrt[c^2 - 4 x^2]), {c, -30, 30, 2}], 
Table[1/2 (c + Sqrt[c^2 - 4 x^2]), {c, -30, 30, 2}]}, {x, -30, 30},
PlotRange -> {{-30, 30}, {-15, 15}}, PlotStyle -> Green, 
AspectRatio -> Automatic]

enter image description here

Thank you in advance!

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Perhaps:

ParametricPlot[
  Table[sign (i {Cos[x], Sin[x]} + {0, i}), {i, 1, 20, 2}, {sign, {-1, 1}}],
  {x, 0, 2 Pi},
  PlotStyle -> Green
]

Mathematica graphics

You can then adjust the PlotRange, the range of and pitch of the values of $i$ to your desired results:

ParametricPlot[
  Table[sign (i {Cos[x], Sin[x]} + {0, i}), {i, 1, 15, 1}, {sign, {-1, 1}}],
  {x, 0, 2 Pi},
  PlotStyle -> Green,
  PlotRange -> {{-30, 30}, {-15, 15}}, ImageSize -> Large
]

Mathematica graphics

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  • $\begingroup$ Thank you for your answer. However, I need to keep the equations 1/2 (c - Sqrt[c^2 - 4 x^2]) 1/2 (c + Sqrt[c^2 - 4 x^2] as this is a math assignment. What I'm mainly looking for is to have plot evaluate the equation at a value of c that will make it a straight line across the x-axis (like in my above picture with the red and green curves) without it appearing messy. $\endgroup$ – Alan Mar 19 '16 at 2:59

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