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