CoCalc Public Files201-303-AH / Fichiers Sage pour les Étudiants / Exercice 11 p 142.sagewsOpen with one click!
Author: Julien Giol
Description: Fichiers Sage
Compute Environment: Ubuntu 18.04 (Deprecated)
%md # Paraboloïde elliptique

Paraboloïde elliptique

var('x, y, z')
(x, y, z)
eq = x==y^2+4*z^2 show(eq)
x=y2+4z2\displaystyle x = y^{2} + 4 \, z^{2}
r = 2 G = implicit_plot3d(eq, (x, -r, r), (y, -r, r), (z, -r, r), plot_points=30, color='orange', mesh=1, opacity=.7) show(G, spin=1)
3D rendering not yet implemented
%md # Traces dans les plans x = k

Traces dans les plans x = k

var('x, y, z') x=0 eq = x==y^2+4*z^2 show(eq)
(x, y, z)
0=y2+4z2\displaystyle 0 = y^{2} + 4 \, z^{2}
r = 5 G = implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red') show(G)
for k in range(1,10): x = k eq = x==y^2+4*z^2 G+= implicit_plot(eq, (y, -r, r), (z, -r, r), color = 'red') show(G)
%md # Traces dans les plans y = k

Traces dans les plans y = k

var('x, y, z') y=0 eq = x==y^2+4*z^2 show(eq)
(x, y, z)
x=4z2\displaystyle x = 4 \, z^{2}
r = 10 G = implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue') show(G)
for k in range(1,4): y = k eq = x==y^2+4*z^2 G+= implicit_plot(eq, (x, -r, r), (z, -r, r), color = 'blue') show(G)
%md # Traces dans les plans z = k

Traces dans les plans z = k

var('x, y, z') z=0 eq = x==y^2+4*z^2 show(eq)
(x, y, z)
x=y2\displaystyle x = y^{2}
r = 10 G = implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'orange') show(G)
for k in range(-1,5): z = k eq = x==y^2+4*z^2 G+= implicit_plot(eq, (x, -r, r), (y, -r, r), color = 'orange') show(G)