Intermediate Algebra Conic Sections

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Intermediate Algebra

10. Conic Sections

Description

At this point, we now investigate other forms of equations to graph. In this topic, we explore equations, now to graph and information about circles; parabolas; ellipses; and hyperbolas. We further explore nonlinear systems of equations and inequalities.

Sections in this topic include:

1. Circles

The first conic section we investigate is circles. Our focus is by given either equations of circles, centers and radii or a graph, we could find all information about the circle and produce it's graph. Groups within this section include: Finding the coordinates of midpoints of segments; finding the center and radius of a circle then graphing the circle; writing the standard form of a circle; determining the center and radius of a circle by completing the square; writing equations of circles given conditions.

2. Parabolas

Our next conic section of study is parabolas. Given either information, or an equation, or a graph, produce all information and graphs of a parabola including the equation of an axis of symmetry.

3. Ellipses

Another conic section of study is an ellipse. Given either information, or an equation, or a graph, produce all information and graphs of an ellipse. The group within this section is: finding the equation of an ellipse from a graph.

4. Hyperbolas

The last conic section of interest is the study of hyperbolas. Given either information, or an equation, or a graph, produce all information and graphs of an ellipse.

5. Solving Nonlinear Systems of Equations

This section investigates solving nonlinear systems of equations by both using the substitution method and by exploring the number of solutions by graphing the various equations as conic sections.

6. Solving Nonlinear Systems of Inequalities

We conclude this topic investigating regions of solutions in nonlinear system of inequalities by graphing the inequalties as conic sections and testing points of solutions.

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