Plot3D[x^2/9-y^2/4,{x,-40,40},{y,-40,40}]

ContourPlot3D[(x^2+y^2+z^2)^2-4(z^2-x^2-y^2)==0,{x,-2,2},{y,-2,2},{z,-2,2}]

ParametricPlot3D[{2Sin[u]*Cos[u]*Cos[v]/(1+(Sin[u])^2),2Sin[u]*Cos[u]*Sin[v]/(1+(Sin[u])^2),2Cos[u]/(1+(Sin[u])^2)},{u,0,Pi},{v,0,2Pi}]

ParametricPlot3D[{u^2,u*v,v},{u,-1,1},{v,-1,1}]

ParametricPlot3D[{u,v^2,u*v^3},{u,-1,1},{v,-1,1}]

p[u_,v_]={u,v^2,u*v^3}

dpdu[u_,v_]=D[p[u,v],u]

dpdv[u_,v_]=D[p[u,v],v]

Jacp[u_,v_]=Transpose[{dpdu[u,v],dpdv[u,v]}]

MatrixForm[Jacp[u,v]]

Det[{{1,0},{0,2 v}}]

Det[{{1,0},{(v^3),3 u (v^2)}}]

w1=ParametricPlot3D[{3u^4+u^2*v,4u^3+2*u*v,v},{u,-1,1},{v,-1,1}]

q[u_,v_]={3u^4+u^2*v,4u^3+2*u*v,v}

dqdu[u_,v_]=D[q[u,v],u]

dqdv[u_,v_]=D[q[u,v],v]

Jacq[u_,v_]=Transpose[{dqdu[u,v],dqdv[u,v]}]

MatrixForm[Jacq[u,v]]

Det[{{12 (u^3)+2 u v,(u^2)},{0,1}}]

Det[{{12 (u^2)+2 v,2 u},{0,1}}]

12 (u^3)+2 u v/.{v-> -6u^2}

q[u,-6*u^2]

w2=ParametricPlot3D[{-3 (u^4),-8 (u^3),-6 (u^2)},{u,-1,1}, PlotStyle->{Red, Thick}]

Show[w1,w2]