Cone[a_] :=
    ContourPlot3D[
    x^2 + y^2 == z^2, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}];
    Plane[a_] := Plot3D[z = a*x + 2, {x, -10, 10}, {y, -10, 10}];
    InterM[a_] :=
    ParametricPlot3D[{t, -Sqrt[(a^2 - 1)*t^2 + 4*a*t + 4],
    1*t + 2}, {t, -10, 10}, PlotStyle -> Thickness[0.02]];
    InterP[a_] :=
    ParametricPlot3D[{t, Sqrt[(a^2 - 1)*t^2 + 4*a*t + 4],
    a*t + 2}, {t, -10, 10}, PlotStyle -> Thickness[0.02]];

    Manipulate[
       Show[
            {Cone[a], Plane[a], InterM[a], InterP[a]}
                                                    ], {a, 0, 2}]