Calculus II

6. Analytic Geometry In the Plane

Description

      We conclude this subject with a preparation into Calculus III by exploring analytic geometry in the plane.  Here, we fully explore the concepts, equations, and graphs of conic sections such as the parabola, ellipse, and hyperbola.  We further investigate translation and rotation of axes.

Sections of this topic include:

1.   Parabolas

      In this section, we investigate the first conic section called parabolas.  Here, given either an equation, a graph, or information (such as a directrix, focus, and/or vertex), we find the equation and graph of a parabola.

2.   Ellipse

     The next conic section of interest is the ellipse.  Again, given either an equation, a graph of information (such as the center, lengths of major or minor exes, foci, or vertices), we find the equation and graph of an ellipse.

3.   Hyperbola

      In this last conic section, we explore the hyperbola.  Given either an equation, a graph or information (such as the center, lengths of the conjugate or transverse axes, vertices or equations of asymptotes), we find the equation and graph of the hyperbola as well as the equations of the asymptotes.

4.   Translation and Rotation of Axes

     In this last section, we explore how graphs of parabolas, ellipses and hyperbolas can be translated or rotated and what their resulting equations would become.