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  Equations of a plane in a coordinate space
         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 of tangency - Condition for a line to be the tangent to a circle
         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 radical line or the radical axis
         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
 
 
 
 
 
 
 
 
 
 
 
Copyright 2004 - 2020, Nabla Ltd.  All rights reserved.