MATHEMATICS   Formulas, Graphs, Tables, . . .  < High School to University Level >
CONTENTS C
COORDINATE GEOMETRY IN 3D
21  Coordinate geometry (or Analytic geometry) in three-dimensional space
Points, lines and planes in three-dimensional coordinate system represented by vectors

Equations of a line in space

The vector's equation of a line
The parametric equations of a line
Equation of a line defined by direction vector and a point - Symmetric equation of a line
Line given by two points
Orthogonal projection of a line in 3D space onto a coordinate plane
Lines in 3D coordinate system represented by vectors examples
Angle between lines
Condition for intersection of two lines in a 3D space
22
The equation of a plane in a 3D coordinate system
General equation of a plane in 3D space
The Hessian normal form of the equation of a plane
The intercept form of the equation of a plane
The distance between a point and a plane - plane given in Hessian normal form
Comparison of general form and the Hessian normal form of equations of a plane
The distance of a point to a plane - plane given in general form
Angle (dihedral angle) between two planes
Planes in 3D coordinate system represented by vectors examples
23  Line and plane in three-dimensional coordinate system represented by vectors
The line of intersection of two planes
Projection of a line onto coordinate planes
How determine two planes of which, a given line is their intersection line
Intersection point of a line and a plane
Sheaf or pencil of planes
The angle between line and plane
24  Point line and plane - orthogonal projections, distances, perpendicularity of line and plane
Through a given point pass a line perpendicular to a given plane
Given a line and a point, through the point lay a plane perpendicular to the line
Projection of a point onto a plane
Projection of a point onto a line
Through a given point lay a line perpendicular to a given line
Projection of a line onto a plane
25  Plane laid through a given point, such that be parallel with two skew lines
Plane laid through a given point, such that be parallel with two parallel lines
Distance between point and line
Distance between parallel lines
Distance between two skew lines
ANALYTIC GEOMETRY - CONIC SECTIONS
26  Conics, a family of similarly shaped curves
Circle
General equation of a circle with the center S(p, q) - translated circle
Equation of the circle with the center at the origin O(0, 0)
Circle through three points
Circle and Line
Line circle intersection
Equation of a tangent at a point of a circle with the center at the origin
Equation of a tangent at a point of a translated circle
27
Condition for a line to be the tangent to the circle with center at the origin O(0, 0)
Condition for a line to be the tangent to the translated circle
Angle between a line and a circle
Mutual position of two circles
The pole and the polar
Angle between two circles
28  Ellipse
Ellipse, definition and construction, eccentricity and linear eccentricity
Constructions of an ellipse
Equation of the ellipse, standard equation of the ellipse
The parametric equations of the ellipse
Equation of a translated ellipse
29  Ellipse and line
Intersection of ellipse and line - tangency condition
Equation of the tangent at a point on the ellipse
Construction of the tangent at a point on the ellipse
Angle between the focal radii at a point of the ellipse
Tangents to an ellipse from a point outside the ellipse - use of the tangency condition
Construction of tangents from a point outside the ellipse
Polar and pole of the ellipse
30  Hyperbola
Definition and construction of the hyperbola
Construction of the hyperbola
Equation of the hyperbola
Examining equation of the hyperbola
Conjugate hyperbola