Study of Straight Lines and Conics

Through the following button you can perform a complete study of the equation of a line or a conic (circumference, parabola, ellipse, hyperbole)

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Math
● Le espressioni si possono inserire solamente tramite la tastiera dell'app
● Il campo nel quale sarà inserita l'espressione è quello evidenziato in giallo
● Il campo in cui inserire l'espressione si seleziona semplicemente facendo click su di esso. Il campo diventerà così evidenziato in giallo
● Non è possibile comporre parole arbitrarie in quanto inserendo le lettere dell'alfabeto verrà inserito uno spazio dopo di essa per cui ogni lettera sarà riconosciuta come una variabile a se
● Inserendo le varie funzioni predefinite verrà inserito il suo nome e quando si cancella questo elemento verrà cancellato l'intero nome
key C
Cancella l'intera espressione
key CE
Cancella l'ultima espressione inserita
key left arrow
Sposta il cursosre di un'espressione a sinistra
key right arrow
Sposta il cursosre di un'espressione a destra

Examples of studies

What is the study of a line or a conic?

Here are some examples (click on the images to view the relevant study):

Study of the equation of a line

Line

Study of the equation of a conic: Parabola with axis parallel to the y axis

Parabola with axis parallel to the y axis

Study of the equation of a conic: Parabola with axis not parallel to any of the Cartesian axes

Study of the equation of a conic: Parabola with axis not parallel to any of the Cartesian axes

Study of the equation of a conic: Ellipse with axes parallel to the Cartesian axes

Ellipse with axes parallel to the Cartesian axes

Study of the equation of a conic: Hyperbola with axes parallel to the Cartesian axes

Hyperbola with axes coinciding with the Cartesian axes

Study of a line

  • Equazioni nelle seguenti forme:

    • explicit
    • implied
    • segmental
    • parametric

  • Intersections with Cartesian axes

  • Angular coefficient

  • Angle formed with the x axis

  • Graphic

Study of a conic

  • Matrix representation

  • Eigenvalues and eigenvectors

  • Vertices

  • Fires

  • Center

  • Axes

  • Direttricides

  • Intersections with Cartesian axes

  • Graphic

Entering expressions

  • The equations (lines and conics) can be inserted either explicitly or implicitly
  • Parameters can not be entered in the equations, so only the letters x and y must appear
  • The product between two letters can be indicated with the asterisk symbol (*) or leaving a space between the letters.If you write two or more letters below, it is not interpreted as a product but as a single variable (x * y = produced between x and y, x y = produced between x and y; xy = the only variable called xy)

You can test different input forms by copying the text in red in the image captions and pasting it into the data entry window that appears by clicking the button at the top of the page to run the equation study (Study of lines and conics).

Example of entering the equation of a straight line in explicit form

equation of a straight line in explicit form y=1/4x-1

Example of data entry: equation of the straight line in an implicit form

Example of data entry: equation of the straight line in an implicit form
2x+sqrt(3)y-1=0

Complete second degree equation in x y (conical)

Complete second degree equation in x y (conical)
x^2+x y-y^2-x=0

Example of entering the equation of a parabola with axis parallel to the x axis

Example of entering the equation of a parabola with axis parallel to the x axis
x=y^2-1

Examples of development carried out by the system (click on the image to see the related course):

Piano Cartesiano: Distanza tra due punti

DISTANCE BETWEEN TWO POINTS: The system uses the appropriate formula by checking whether the two points have common coordinates or not.

Medium Point: the system recognizes if the points have some co-ordination in common and in case adapts the application of the formulas to the data provided

Medium Point: the system recognizes if the points have some co-ordination in common and in case adapts the application of the formulas to the data provided

Piano cartesiano: Intersezione tra due curve

Cartesian plane: Intersection between two curves

Cartesian Plan: Baricenter of a Triangle

BARICENTER OF A TRIANGLE: The system directly applies the formula to determine the center of gravity

Cartesian plane: Circumference of a Triangle

CIRCOCENT OF A TRIANGLE: The system calculates two axes of the triangle and intersects them to find the circumcentre

Cartesian Plan: Orthocenter of a Triangle

ORTOCENTRO OF A TRIANGLE: The system calculates two heights of the triangle and intersects them to find the orthocenter

Study of Straight Lines and Conics ultima modifica: 2018-08-04T04:45:12+00:00 da roberto