Les coniques

Synthèse sur les coniques

Définition géométrique :
Foyer, directrice, excentricité

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Définition analytique :
Ensemble des points M(x;y)  tels que : \( ax^2+bxy+cy^2+\alpha x+\beta y+\gamma=0 \)
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Pour saisir une nouvelle équation, taper par exemple dans la barre de saisie : d:x^2+3*x+2*y^2-4=0
Si le point M disparait, taper : M=Point[d]

Syntaxe Xcas : reduced_conic(2*x^2+2*x*y+2*y^2+5*x+3,[x,y])
Renvoie une liste d'éléments :

Outil Wolfram :



Calculs sur Wiris pour retrouver les foyers, les génératrices et l'excentricité:
\( Ax^2+Bxy+Cy^2+\alpha x + \beta y + \gamma =0 \Leftrightarrow (x-x_F)^2+(y-y_F)^2=e^2 (ax+by+c)^2 \) et \( a^2+b^2=1 \)

Equation polaire d'une conique
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Equation réduite d'une ellipse
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Equation réduite d'une parabole
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Equation réduite d'une hyperbole
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