About Analytic Geometry

We study vectors, lines in two dimensions, circles, conics, transformation of coordinates, polar coordinates, parametric equations, and solid analytic geometry of vectors, lines, planes, cylinders, shperical and cylindrical coordinates.

Parabolas. In general, a parabola is a conic sections that can generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. In this topic we define a parabola as locus of points which are equidistant from a given point (the focus) and a given line (the directrix). We illustrate the definition with several examples including how to find an equation of a parabola given some geometric information. Conversely, we also show how to find the vertex, directrix, and focus given the equation of the parabola.

Ellipses. In general, an ellipse is a type of conic section that can be generated if a conical surface is cut with a plane which does not intersect the cone's base, then intersection of the cone and plane is an ellipse. In this topic we define an ellpise as locus of points where the sum from any point on the curve to two fixed points (the foci) is a positive constant. We illustrate the definition with several examples including how to find an equation of an ellipse given some geometric information. Conversely, we also show how to find the vertices, major axis, minor axis, eccentricity, and focus given the equation of the ellipse.

Hyperbolas. In general, a hyperbola is a type of conic section defined by the intersection of a right circular conical surface and a plane which cuts through both halves of the cone. In this topic we define a hyperbola as locus of points where the difference from any point on the curve to two fixed points (the foci) is a positive constant. We illustrate the definition with several examples including how to find an equation of a hyperbola given some geometric information. Conversely, we also show how to find the vertices, major axis, minor axis, eccentricity, and focus given the equation of the hyperbola.

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Cite this as:
About Analytic Geometry
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/about-analytic-geometry.html