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Chapter 11

Conic Sections

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
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Section 1
Introduction to Conic Sections
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What Are Conic Sections?

Conic sections are obtained by the intersection of the surface of a cone with a plane, and have certain features.

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Eccentricity

Every conic section has a constant eccentricity that provides information about its shape.

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Types of Conic Sections

Conic sections are formed by the intersection of a plane with a cone, and their properties depend on how this intersection occurs.

Section 2
The Parabola
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Parabolas As Conic Sections

Parabolas are one of the four shapes known as conic sections, and they have many important real world applications.

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Applications of the Parabola

Parabolas have important applications in physics, engineering, and nature.

Section 3
The Circle and the Ellipse
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Introduction to Circles

The equation for a circle is an extension of the distance formula.

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Introduction to Ellipses

Understand the equation of an ellipse as a stretched circle.

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Parts of an Ellipse

Ellipses are one of the types of conic sections. The specific features of an ellipse can be determined from its equation.

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Applications of Circles and Ellipses

Circles and ellipses are encountered in everyday life, and knowing how to solve their equations is useful in many situations.

Section 4
The Hyperbola
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Introduction to Hyperbolas

Hyperbolas are one of the four conic sections, and are described by certain kinds of equations.

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Parts of a Hyperbola

The features of a hyperbola can be determined from its equation.

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Applications of Hyperbolas

A hyperbola is an open curve with two branches and a cut through both halves of a double cone, which is not necessarily parallel to the cone's axis.

Section 5
Nonlinear Systems of Equations and Inequalities
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Nonlinear Systems of Equations and Problem-Solving

As with linear systems, a nonlinear system of equations (and conics) can be solved graphically and algebraically for all of its variables.

Models Involving Nonlinear Systems of Equations

Nonlinear systems of equations can be used to solve complex problems involving multiple known relationships.

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Nonlinear Systems of Inequalities

Systems of nonlinear inequalities can be solved by graphing boundary lines.

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Boundless Algebra by Boundless
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Conic Sections
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