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Conic Sections: Types & Examples

The document provides an overview of the different types of conic sections: circles, ellipses, parabolas, hyperbolas, and degenerate cases. Circles are formed when the plane is horizontal to the cone. Ellipses are bounded curves formed by one cone intersection. Parabolas are unbounded curves formed by a single cone intersection, like the trajectory of a thrown ball. Hyperbolas have two unbounded branches from intersecting both cones, seen in hourglasses. Degenerate cases result in points, lines, or two lines from plane-cone intersection.

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Dominic Rago
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196 views2 pages

Conic Sections: Types & Examples

The document provides an overview of the different types of conic sections: circles, ellipses, parabolas, hyperbolas, and degenerate cases. Circles are formed when the plane is horizontal to the cone. Ellipses are bounded curves formed by one cone intersection. Parabolas are unbounded curves formed by a single cone intersection, like the trajectory of a thrown ball. Hyperbolas have two unbounded branches from intersecting both cones, seen in hourglasses. Degenerate cases result in points, lines, or two lines from plane-cone intersection.

Uploaded by

Dominic Rago
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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The Conic Sections: An Overview

Conic sections, or conics, are curves obtained by the intersection of a plane and a cone. Conics
can be found in nature and have many applications in other fields. Conic sections can be identified as
circles, parabolas, ellipses, hyperbolas, and degenerate cases.

Let us now look at each conic section and how they are formed.

Circle

A circle is formed a conic section which is formed when the plane is horizontal as it intersects the cone.

There are many real-life representations of a circle. A regular round pizza, Ferris wheel, and the face of a
coin are among the numerous examples of a circle.

Ellipse

An ellipse is formed when the (tilted) plane intersects only one cone to form a bounded curve.

Parabola

A parabola is formed when the plane intersects only one cone to form an unbounded curve. The
trajectory of a ball thrown upward forms a parabola. Parabola has many applications in real life
including in the field of architecture and manufacturing.

Hyperbola

Hyperbola, also a conic section, is formed when the plane (not necessarily vertical) intersects both cones
to form two unbounded curves (each called a branch of the hyperbola).

An hour glass that contains two hyperbolas, one in each side, is a real-life representation of a hyperbola.

Degenerate Cases

A point, one line, and two lines are also formed when a plane and cone intersect. They are referred to as
degenerate cases.

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