Question

I can plot the curve corresponding to an implicit equation:

ContourPlot[x^2 + (2 y)^2 == 1, {x, -1, 1}, {y, -1, 1}]

But I cannot find a way to color the contour line depending on the location of the point. More precisely, I want to color the curve in 2 colors, depending on whether x² + y² < k or not.

I looked into ColorFunction but this is only for coloring the region between the contour lines.
And I was not able to get ContourStyle to accept a location-dependent expression.

Answer 1

you could use RegionFunction to split the plot in two:

Show[{
  ContourPlot[x^2 + (2 y)^2 == 1, {x, -1, 1}, {y, -1, 1}, 
  RegionFunction -> Function[{x, y, z}, x^2 + y^2 < .5], 
  ContourStyle -> Red], 
  ContourPlot[x^2 + (2 y)^2 == 1, {x, -1, 1}, {y, -1, 1}, 
  RegionFunction -> Function[{x, y, z}, x^2 + y^2 >= .5], 
  ContourStyle -> Green]
}]