Well there is a nice way to extract points:
mYcp = ContourPlot[x^2 + y^2 == 6, {x, -3, 3}, {y, -3, 3}]

Short[Cases[Normal@mYcp, Line[x_] :> x, Infinity], 20]
{{{-1.07143,-2.20209},{-1.1106,-2.18203},{-1.17857,-2.14721},{-1.18634,-2.14286},{-1.24885,-2.10599},{-1.28571,-2.08271},{-1.38018,-2.02304},{-1.47143,-1.95714},{-1.5,-1.93609},{-1.50433,-1.9329},{-1.50952,-1.92857},{-1.62121,-1.8355},{-1.71429,-1.7479},{-1.7316,-1.7316},{-1.7479,-1.71429},<<246>>,{-0.289216,-2.43207},{-0.321429,-2.42778},{-0.363553,-2.42216},{-0.383423,-2.41914},{-0.428571,-2.41111},{-0.473545,-2.40212},{-0.634454,-2.36555},{-0.642857,-2.36335},{-0.647783,-2.36207},{-0.663265,-2.35714},{-0.857143,-2.29252},{-0.961538,-2.25275},{-0.965438,-2.25115},{-0.968045,-2.25},{-1.07143,-2.20209}}}