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MATHEMATICS Formulas, Graphs,
Tables, . . . < High School to University Level > |
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CONTENTS C
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COORDINATE GEOMETRY IN 3D
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21
Coordinate geometry
(or Analytic geometry) in three-dimensional space
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Points, lines and planes in three-dimensional coordinate
system represented by vectors
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Equations of a line in space
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The
vector's equation of a line
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The parametric equations of a line
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Equation of a line defined by
direction vector and a point - Symmetric equation of a line
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Line given by two points
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Orthogonal projection of a line
in 3D space onto a
coordinate
plane
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Lines in 3D coordinate system
represented by vectors examples
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Angle between lines
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Condition for intersection of two
lines in a 3D space
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22
Equations of a plane in a coordinate space
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The equation of a
plane in
a
3D coordinate system
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General equation of a plane in 3D
space
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The Hessian normal form of the
equation of a plane
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The intercept form of the equation of a
plane
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The distance between a point and a
plane - plane given in Hessian normal form
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Comparison of general form and the
Hessian normal form of equations of a plane
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The distance of a point to a plane -
plane given in general form
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Angle (dihedral angle) between two
planes
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Planes in 3D coordinate system
represented by vectors examples
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23
Line and plane in three-dimensional coordinate
system represented by vectors
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The line of intersection of two planes
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Projection of a line onto coordinate planes
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How determine two planes of which, a given line is their
intersection line
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Intersection point of a line and a plane
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Sheaf or
pencil of planes
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The angle between line and plane
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24
Point line and plane - orthogonal
projections, distances, perpendicularity of line and plane
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Through a given point pass a line perpendicular to
a given plane
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Given a line and a point, through
the point lay a plane
perpendicular to the line
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Projection of a point onto a plane
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Projection of a point onto a line
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Through a given point lay a line perpendicular to a given line
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Projection of a line onto a plane
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25
Plane laid through a given point, such that be parallel with two skew lines
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Plane
laid through a given point, such that be parallel with two parallel
lines
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Distance between point and line
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Distance between parallel lines
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Distance between two skew lines
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ANALYTIC
GEOMETRY - CONIC
SECTIONS
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26
Conics,
a family of similarly shaped curves
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Circle
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General equation of a circle with the center
S(p, q)
- translated circle
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Equation of the circle with the
center at the origin
O(0,
0)
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Circle through three points
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Circle
and Line
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Line circle intersection
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Equation of a tangent at a point of a circle with the center at the
origin
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Equation of a tangent at a point
of a translated circle
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27
Condition of tangency - Condition for a line to be the tangent to a circle
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Condition for a line to be the tangent to the circle with center at the
origin
O(0, 0)
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Condition for a line to be the tangent to the translated circle
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Angle between a line and a circle
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Mutual position of two circles
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The radical line or the radical axis
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The pole and the polar
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Angle between two circles
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28
Ellipse
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Ellipse,
definition and construction, eccentricity and linear
eccentricity
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Constructions of an ellipse
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Equation of the ellipse, standard
equation of the ellipse
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The parametric equations of the
ellipse
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Equation of a translated ellipse
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29
Ellipse and line
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Intersection of ellipse and line - tangency condition
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Equation of the tangent at a point on the ellipse
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Construction of the tangent at a point on the ellipse
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Angle between the focal radii at a point of the ellipse
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Tangents to an ellipse from a
point outside the ellipse - use of the tangency condition
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Construction of tangents from a point outside the ellipse
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Polar and pole of the ellipse
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30 Hyperbola
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Definition and construction
of the hyperbola
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Construction of the hyperbola
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Equation of the hyperbola
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Examining equation of the hyperbola
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Conjugate
hyperbola
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