Analytic Geometry

Coordinate systems, distance formula, midpoint formula, slope, angle between lines, symmetry, and area of polygons.

Equations of lines, slopes, intercepts, distances, and angles between lines.

Equations of circles, finding center and radius, tangent lines, and degenerate cases.

Equations of parabolas, vertex, focus, directrix, and applications.

Equations of ellipses, finding foci, vertices, eccentricity, and area.

Equations of hyperbolas, finding foci, vertices, transverse axis, asymptotes, and eccentricity.

Polar coordinate system, conversion between rectangular and polar, and graphing polar curves.

Transformation of coordinates through translation and rotation of the axes, and eliminating the xy-term in conic sections.

Defining curves using an independent parameter, converting to rectangular form, and applications to conic sections.

Three-dimensional coordinate systems, distance, direction cosines, equations of lines and planes in space.

Understanding 3D surfaces including spheres, ellipsoids, paraboloids, and hyperboloids.

Equations of tangent and normal lines to circles, parabolas, ellipses, and hyperbolas.

Introduction to vectors, dot product, cross product, and their applications in analytic geometry.

Advanced 3D coordinate systems and their relationship with rectangular coordinates.

Analysis of advanced planar curves including cycloids, epicycloids, hypocycloids, and lemniscates.