Uogolnienie

r = 0.1;
x0 = 0.7;
y0 = 0.3;
z0 = powierzchnia[x0, y0];
listaKatow = Table[RandomReal[{0, 2 Pi}], {i, 100}];
powierzchnia[x_, y_] = 2 x + 3 y^2;
f[x_, y_, xp_, yp_,
   zp_] = (x - xp)^2 + (y - yp)^2 + (2 x + 3 y^2 - zp)^2 - r^2;

alfa = listaKatow[[1]];

Result = Solve[{x, y} \[Element]
     InfiniteLine[{{x0, y0}, {x0 + Cos[alfa], y0 + Sin[alfa]}}] &&
    f[x, y, x0, y0, z0] == 0, {x, y}];

xPunktu = Result[[1, 1, 2]];
yPunktu = Result[[1, 2, 2]];
zPunktu = powierzchnia[xPunktu, yPunktu];

xPunktu2 = Result[[2, 1, 2]];
yPunktu2 = Result[[2, 2, 2]];
zPunktu2 = powierzchnia[xPunktu2, yPunktu2];

dlugosc = Sqrt[(xPunktu - x0)^2 + (yPunktu - y0)^2 + (zPunktu - z0)^2]
dlugosc2 =
 Sqrt[(xPunktu2 - x0)^2 + (yPunktu2 - y0)^2 + (zPunktu2 - z0)^2]

Show[
 ContourPlot[{y*Cos[alfa] - x*Sin[alfa],
   f[x, y, x0, y0, z0] == 0}, {x, -2., 2.}, {y, -2., 2.}],
 Graphics[{{Blue,
    InfiniteLine[{{x0, y0}, {x0 + Cos[alfa], y0 + Sin[alfa]}}]}, {Red,
     Point[{x, y}] /. Result}}]
 ]

Show[
 Plot3D[{2 x + 3 y^2}, {x, -1, 1}, {y, -1, 1}, BoxRatios -> {1, 1, 1}],
 Graphics3D[{Red, PointSize[.02], Point[{x0, y0, z0}]}],
 Graphics3D[{Green, PointSize[.02],
   Point[{xPunktu, yPunktu, zPunktu}]}],
 Graphics3D[{Blue, PointSize[.02],
   Point[{xPunktu2, yPunktu2, zPunktu2}]}],
 Graphics3D[{Opacity[0.5], Sphere[{x0, y0, z0}, r]}]
 ]