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  • 2 месяца назадОпубликованоEducation in Engineering with Arijit Banerjee

Beautiful Visualization of Conic Sections | GeoGebra 3D Animation

This video demonstrates the different conic sections. How they are generated from the sections of planes oriented at different angles with the double cone is visualised with the help of this video. Different conic sections are made visible with the help of the intersection between the cone/ double-cone and the plane. For eample, when the cutting plane is perpendicular to the axis of the cone or parallel to the base of the cone, the intersection is a circle. When the cutting plane is parallel to the inclined curved surface, the intersection is a parabola. For any other orientation, in between, the conic section is an ellipse. These features are nicely demonstrated here in this video. — this video demonstrates how different cutting planes intersect a double right circular cone to form Circle, Ellipse, Parabola, and Hyperbola. No narration — only clean, smooth visual geometry using GeoGebra Classic 3D view. 🌀 Concepts shown in this video: Generation of Circle by a plane ⟂ cone axis Formation of Ellipse by an oblique plane cutting one nappe Creation of Parabola by a plane parallel to a generator Visualization of Hyperbola by a plane cutting both nappes Visualisation of a Rectangular Hyperbola (for the half-cone angle = 45°) with cutting plane parallel to the cone-axis) 📘 Software Used: GeoGebra Classic 🎥 Type: Silent 3D Animation | Educational Geometry Visualization 📚 Ideal for: Students of Mathematics, Engineering, and Architecture | Teachers & Educators 👉 Watch till the end to see how the shape of the section changes with the angle of inclination of the cutting plane. If you like this visual approach, Subscribe for more animations on Analytical Geometry, Calculus, and Mechanics using GeoGebra. ⏱️ Timestamps: 0:00 Circle 0:58 Rectangular Hyperbola (for half-cone angle = 45°) 1:47 Parabola 2:48 Parabola (from another side) 3:39 Ellipse 4:25 All together 5:16 Hyperbola (general: any angle between Rectangular Hyperbola and Parabola) 6:46 Finally all curves together 🔔 Don’t forget to Like 👍 | Comment 💬 | Share 📢 | Subscribe ❤️