var('t')
t
r=vector((t,2-t,4*t+1))
r
parametric_plot3d(r,(0,10))

var('t')
t
r=vector((2*sin(t),3*cos(t),-t))
r
parametric_plot3d(r,(-10,10))

var('t')
t
r=vector((2*sin(t),3*cos(t),sin(8*t)))
r
parametric_plot3d(r,(-20,20))

var('t')
t
r=vector((t*sin(t),t*cos(t),sin(8*t)))
r
parametric_plot3d(r,(-20,20))

var('t')
t
r=vector((t*sin(t),t*cos(t),t*sin(3*t)))
r
parametric_plot3d(r,(-20,20))

var('t')
t
r=vector((2*sin(3*t)*cos(t),2*sin(3*t)*sin(t),sin(3*t)))
r
parametric_plot3d(r,(-5,5))

var('x,y,z')
S=implicit_plot3d(x^2+y^2+z^2==5,(x,-3,3),(y,-3,3),(z,-3,3),opacity=0.5)
var('t')
t
r=vector((sin(t),cos(t), t))
r
C=parametric_plot3d(r, (-5,5))
show(C+S)

var('x,y,z')
S=implicit_plot3d(x^2+y^2==4,(x,-5,5),(y,-5,5),(z,-5,5),opacity=0.5)
r=implicit_plot3d(z==x^2,(x,-5,5),(y,-5,5),(z,-5,5),opacity=0.5)
var('t')
M=vector((2*sin(t),2*cos(t), 4*(sin(t))^2))
C=parametric_plot3d(M, (-5,5), color='red')
show(r+S+C)

var('x,y,z')
S=implicit_plot3d(z==x+y,(x,-5,5),(y,-5,5),(z,-5,5),opacity=0.5)
r=implicit_plot3d(4*x^2+y^2==4,(x,-5,5),(y,-5,5),(z,-5,5),opacity=0.5)
var('t')
M=vector((sin(t),2*cos(t), sin(t)+2*cos(t)))
C=parametric_plot3d(M, (-5,5), color='red')
show(r+S+C)

ar('t')
var('t')
M=vector((exp(t),t*exp(t), t*exp(t^2)))
N=vector((1+t,t,t))
C=parametric_plot3d(M, (-1/2,1/2),color='red')
D=parametric_plot3d(N, (-1,1), color='blue')
show(D+C)

︠58b5ce89-7c84-4a4d-a71c-c3a25bcf22c3s︠
var('x,y')
M=vector((x,1/2*x^2))
C=parametric_plot(M, (-3,3),color='red')
D=implicit_plot(x^2+(y-1)^2==1, (x,-1,1),(y,0,2), color='blue')
R=implicit_plot((x+1)^2+(y-5/2)^2==8, (x,-5,3),(y,-2,5), color='green')
show(D+C+R)

var('t')
t
r=vector((t,2*cos(t),sin(t)))
r
R=parametric_plot3d(r,(-10,10))
N=vector((1+t,t,t))
D=parametric_plot3d(N, (-1,1), color='blue')
show(R+D)