Introduction to Conic Section

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Learning Objectives:

Understand and apply Conic Sections.

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Some terminologies related to a Cone:

1.    Axis: The fixed line is called the Axis of the cone.

2.    Vertex: The Vertex is the point sharedby both cones.

3.    Generators: The lines that pass through the Vertex and form the cones are the Generators.The Generators lie in the cone.

4.    Nappes: The cone consists of two parts called the Nappes.

Conic Section:

A Conic Section is a curve generated by intersecting a Right Circular Cone with a plane.

Some basic figures constructed by Conic Section:

1.    Circle: A Circle is generated when the plane is perpendicular to the axis of the cone.

2.    Ellipse: An Ellipse is generated when the plane is tilted so it intersects each Generator, but only intersects one Nappe.

3.    Parabola: A Parabola is generated when the plane is tilted so it is parallel to one Generator only intersects one Nappe.

4.    Hyperbola: A Hyperbola is generated when the plane intersects both Nappes.

 

 

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Hook question:

1.    What are Axis and Vertex of a cone?

2.    What is Generator and Nappe of a cone?

3.   What is a Conic Section?

4.   How are the following formed by Conic Section?

Circle, Ellipse, Parabola & Hyperbola

 

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