# Plotting a table with varying step sizes

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

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]


Perhaps:

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


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
]


• 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.
– Alan
Commented Mar 19, 2016 at 2:59