
MATHEMATICS Formulas, Graphs,
Tables, . . . < High School to University Level > 

CONTENTS C


COORDINATE GEOMETRY IN 3D

21
Coordinate geometry
(or Analytic geometry) in threedimensional space

Points, lines and planes in threedimensional 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 threedimensional 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

















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