Website owner:  James Miller

Solid Analytic Geometry

Directed line segment, direction angle, direction cosine, direction number

Equations of a plane: general, normal, intercept and three-point forms. Equations of a line: parametric, symmetric and two-point form. Traces, intercepts, pencils.

Cylindrical and spherical coordinates

Surface of revolution, cylindrical surface, cylinder, directrix, generatrix, conical surface, pyramidal surface

General equation of the second degree, quadric surfaces, reduction to canonical form, the 17 canonical forms, transformation of coordinates

The function f(x, y, z) and associated matrices E and e

Diameters and diametral planes

Centers of the quadric surfaces

Derivation of equations for diametral planes and centers

Changes in equation coefficients produced by translation and rotation of the coordinate system

Simplification of the general equation of the second degree by translation

Reduction of the general equation of the second degree to canonical form

Principal planes and eigenvectors

Quadratic forms, canonical forms of quadric surfaces with centers

Equations relating the canonical system coordinates to the expressions for the coordinate planes

Analysis of a quadric surface