Transcript Conic Sections An Introduction

Conic Sections
An Introduction
Conic Sections - Introduction

A conic is a shape
generated by intersecting
two lines at a point and
rotating one line around the
other while keeping the
angle between the lines
constant.
Conic Sections - Introduction
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The resulting collection
of points is called a
right circular cone. The
two parts of the cone
intersecting at the
vertex are called
nappes.
Vertex
Nappe
Conic Sections - Introduction


A “conic” or conic
section is the
intersection of a plane
with the cone.
The plane can intersect
the cone at the vertex
resulting in a point.
Conic Sections - Introduction

The plane can intersect
the cone perpendicular
to the axis resulting in a
circle.
Conic Sections - Introduction

The plane can intersect
one nappe of the cone
at an angle to the axis
resulting in an ellipse.
Conic Sections - Introduction

The plane can intersect
one nappe of the cone
at an angle to the axis
resulting in a parabola.
Conic Sections - Introduction

The plane can intersect two
nappes of the cone
resulting in a hyperbola.