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MATHEMATICS Formulas, Graphs,
Tables, . . . < High School to University Level > |
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CONTENTS D
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31
Equilateral or rectangular
hyperbola
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Translated hyperbola
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Equation of the hyperbola in vertex form
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Parametric equation of the hyperbola
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Equilateral or rectangular hyperbola with the coordinate axes as its
asymptote
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Translation
of equilateral or rectangular hyperbola with the coordinate axes as its
asymptote
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The graph of the translated reciprocal function or the linear rational
function
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32
Hyperbola and line
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Hyperbola and line relationships
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Condition for a line to be the tangent to the hyperbola -
tangency condition
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The equation of the tangent at the point on the hyperbola
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Polar and pole of the hyperbola
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Construction of the tangent at the point on the hyperbola
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Construction of tangents from a point outside the hyperbola
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33
Properties of the hyperbola
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The area of a triangle which the tangent at a point on the hyperbola forms with
asymptotes
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The tangency point bisects the line
segment of the tangent between
asymptotes
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The parallels to the asymptotes through the tangency point intersect asymptotes
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The equation of the equilateral or rectangular hyperbola with the
coordinate axes as its
asymptotes
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34
Parabola
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Definition and construction
of the parabola
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Construction of the parabola
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Vertex form of the equation of a parabola
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Transformation of the equation of a parabola
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Equation of a translated parabola - the standard form
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The parabola whose axis of symmetry is parallel to the y-axis
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Equations of the parabola written in the general form
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Parametric equations of the parabola
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35
Parabola
and line
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Common points of a line and a parabola
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Condition for a line to be the tangent to the parabola
- tangency condition
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The equation of the tangent and the normal at the point on the parabola
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Properties of the parabola
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Properties of the equations of the tangent and the normal of the parabola
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The tangent at any point on the parabola bisects the angle
j between focal distance
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Tangents drawn at the endpoints of a focal chord intersect at right angles on the
directrix
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Polar of the parabola
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36
Construction of the tangent at the point on the parabola and from a point exterior to the parabola
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Parabola and
line examples
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Conics, a
family of similarly shaped curves
- properties of conics
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Dandelin
spheres proof of conic sections focal properties
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Proof that conic section curve is
the ellipse
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Conics, a family of similarly shaped curves
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The equation of conics in
the vertex form
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37
Geometry
and use of trigonometry
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Plane
figures
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Triangle
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Properties of triangles
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Congruence of triangles
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Similarity of triangles
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Right-angled
triangle
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The
Pythagorean theorem
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Trigonometric functions of an acute angle defined in a right triangle
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Solving
the right triangle
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Oblique
or scalene triangle
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The triangle's
circumcircle,
perpendicular bisectors
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The triangle's
incircle, the angle bisector
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The median of triangle,
centroid
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The
altitude of triangle, orthocenter
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Triangle
formulas
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The
sine law
(or the sine rule) and the cosine law
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The
sine law
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The cosine law
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38
Quadrilaterals
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Square
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Rhombus
or rhomb
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Rectangle
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Parallelogram
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Kite
or deltoid
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Trapezium
or trapezoid
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Isosceles
trapezoid
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Cyclic quadrilateral
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Tangential quadrilateral
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Polygons
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Regular
polygons
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39
Circle,
circular sector and circular segment
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Central angle, inscribed angle
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Construction of a tangent
from a point
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Circumference, the length of a circle - the perimeter
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Length of an arc
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Circle and circular sector
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Circular segment
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Annulus and annulus segment
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Solid
geometry, solid figures
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Prism
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Right regular prism
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Cube
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Rectangular prism or
rectangular parallelepiped (cuboid)
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Right triangular prism
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Regular right triangular prism
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Regular right hexagonal prism
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40
Pyramid
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Right regular pyramid
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Regular
square pyramid
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Regular triangular pyramid
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Regular hexagonal pyramid
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Right
pyramidal frustum
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Regular
Polyhedrons
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Tetrahedron
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Octahedron
and icosahedron
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Dodecahedron
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Solids
of revolution
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Cylinder
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Cone
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Conical
frustum
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Sphere
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Spherical cap
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Spherical
segment
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Spherical
sector
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