Intersection of Cylinder and Cone

GeoGebra Commands & Parameters

1. Point({s, t, -5}) → A
2. Point({s, t, 5}) → B
3. Cylinder(Point[{s, (t * cos(θ)) - (h_{Zylinder} * sin(θ)), (t * sin(θ)) + (h_{Zylinder} * cos(θ))}], Point[{s, (t * cos(θ)) + (h_{Zylinder} * sin(θ)), (t * sin(θ)) - (h_{Zylinder} * cos(θ))}], r) → d_2, d_2, d_3, d_4
4. Cone(Point[{0, 0, h_{Kegel}}], Point[{0, 0, 0}], (h_{Kegel} * R)) → k, k_2, k_3
5. Cone(Point[{0, 0, (-h_{Kegel})}], Point[{0, 0, 0}], (h_{Kegel} * R)) → m, m_2, m_3
6. CurveCartesian(f_{up}(η), (cos(θ) * η) - ((sin(θ) * 1 / (((sin((2 * θ)) * (1 + R^(2))) * η))) * (f_{up}(η)^(2) + ((1 - R^(2)) * η^(2)))), (sin(θ) * η) + ((cos(θ) * 1 / (((sin((2 * θ)) * (1 + R^(2))) * η))) * (f_{up}(η)^(2) + ((1 - R^(2)) * η^(2)))), η, t - r, t + r) → γ_u
7. CurveCartesian(f_{down}(η), (cos(θ) * η) - ((sin(θ) * 1 / (((sin((2 * θ)) * (1 + R^(2))) * η))) * (f_{down}(η)^(2) + ((1 - R^(2)) * η^(2)))), (sin(θ) * η) + ((cos(θ) * 1 / (((sin((2 * θ)) * (1 + R^(2))) * η))) * (f_{down}(η)^(2) + ((1 - R^(2)) * η^(2)))), η, t - r, t + r) → γ_d
8. CurveCartesian(0, (t * (-sin(θ))), (t * cos(θ)), t, -24, 24) → c
9. Coefficients(Polynomial[D_0]) → L_0
10. If(Element[L_0, 2]^(2) - ((4 * Element[L_0, 1]) * Element[L_0, 3]) < 0, t, (1 / ((2 * Element[L_0, 1])) * ((-Element[L_0, 2]) - (Element[L_0, 2]^(2) - ((4 * Element[L_0, 1]) * Element[L_0, 3]))^(0.5)))) → η_{01}
11. If(Element[L_0, 2]^(2) - ((4 * Element[L_0, 1]) * Element[L_0, 3]) < 0, t, (1 / ((2 * Element[L_0, 1])) * ((-Element[L_0, 2]) + (Element[L_0, 2]^(2) - ((4 * Element[L_0, 1]) * Element[L_0, 3]))^(0.5)))) → η_{02}
12. CurveCartesian((r^(2) - (η - t)^(2))^(0.5), η, (1 / R * (((2 * t) * η) - t^(2) + r^(2))^(0.5)), η, t - r, t + r) → δ_{uu}
13. CurveCartesian((-(r^(2) - (η - t)^(2))^(0.5)), η, (1 / R * (((2 * t) * η) - t^(2) + r^(2))^(0.5)), η, t - r, t + r) → δ_{du}
14. CurveCartesian((r^(2) - (η - t)^(2))^(0.5), η, (-1 / R * (((2 * t) * η) - t^(2) + r^(2))^(0.5)), η, t - r, t + r) → δ_{ud}
15. CurveCartesian((-(r^(2) - (η - t)^(2))^(0.5)), η, (-1 / R * (((2 * t) * η) - t^(2) + r^(2))^(0.5)), η, t - r, t + r) → δ_{dd}
16. CurveCartesian(f_{up}(η), (η * cos(θ)) - ((sin(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) + D_{sup}(η)^(0.5))), (η * sin(θ)) + ((cos(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) + D_{sup}(η)^(0.5))), η, t - r, t + r) → γ_{uu}
17. CurveCartesian(f_{up}(η), (η * cos(θ)) - ((sin(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) - D_{sup}(η)^(0.5))), (η * sin(θ)) + ((cos(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) - D_{sup}(η)^(0.5))), η, t - r, t + r) → γ_{ud}
18. CurveCartesian(f_{down}(η), (η * cos(θ)) - ((sin(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) + D_{sdown}(η)^(0.5))), (η * sin(θ)) + ((cos(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) + D_{sdown}(η)^(0.5))), η, t - r, t + r) → γ_{du}
19. CurveCartesian(f_{down}(η), (η * cos(θ)) - ((sin(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) - D_{sdown}(η)^(0.5))), (η * sin(θ)) + ((cos(θ) * 1 / ((2 * a))) * ((((1 + R^(2)) * sin((2 * θ))) * η) - D_{sdown}(η)^(0.5))), η, t - r, t + r) → γ_{dd}