Exercice 11 p 142.sagews

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# Paraboloïde elliptique

Paraboloïde elliptique

var('x, y, z')

(x, y, z)

eq = x==y^2+4*z^2
show(eq)

$\displaystyle x = y^{2} + 4 \, z^{2}$

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

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# 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)

$\displaystyle 0 = y^{2} + 4 \, z^{2}$

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)

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# 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)

$\displaystyle x = 4 \, z^{2}$

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)

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# 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)

$\displaystyle x = y^{2}$

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)