2507.sagews

x,y,z=var('x,y,z')
f=implicit_plot3d(z-e^(x^2-y^2)==0,(x,-5,5),(y,-5,5),(z,0,10),opacity=.75)
p=point([1,-1,1],size=10)
g=implicit_plot3d(2*x+2*y-z==-1,(x,-5,5),(y,-5,5),(z,0,10),color='gray')
f+p+g

x,y,z=var('x,y,z')
f=implicit_plot3d(z-sqrt(x+e^(4*y)),(x,1,7),(y,-2,4),(z,0,6),opacity=.75)
p=point([3,0,sqrt(3)],size=10)
g=implicit_plot3d(.25*x+y+1.2-z==0,(x,1,7),(y,-2,4),(z,0,6),color='gray')
f+p+g

x,y,z=var('x,y,z')
f=implicit_plot3d(z-sin(2*x+3*y)==0,(x,-5,5),(y,-5,5),(z,-5,5),opacity=.75)
p=point([-3,2,0],size=10)
g=implicit_plot3d(2*x+3*y-z==0,(x,-5,5),(y,-5,5),(z,-5,5),color='gray')
f+p+g