(*Ellipsoid*)
In[]:=
Solve
2
x
4
+
2
y
+
2
z
9
3,z
Out[]=
z-
3
2
12-
2
x
-4
2
y
,z
3
2
12-
2
x
-4
2
y

​
Ellipsoid1[x_,y_]=-
3
2
12-
2
x
-4
2
y
​​Ellipsoid2[x_,y_]=
3
2
12-
2
x
-4
2
y
Out[]=
-
3
2
12-
2
x
-4
2
y
Out[]=
3
2
12-
2
x
-4
2
y
Point: ( -2 , 1 , -3 )
​
​plane:
Plane[x_,y_]=-
3
2
x+3y-9(*Tangentplanetothepoint(-2,1,-3)*)
Out[]=
-9-
3x
2
+3y
​
= t​​x = - t - 2, y = 2t + 1, z = -2t/3 - 3
​
​
In[]:=
Show[Plot3D[{Plane[x,y],Ellipsoid1[x,y],Ellipsoid2[x,y]},{x,-5,5},{y,-5,5},BoxRatios{1,1,1},AxesLabelAutomatic,PlotRangeFull,Lighting"Neutral"],ParametricPlot3D[{-t-2,2t+1,-2t/3-3},{t,-5,5}]]
Out[]=
​
In[]:=
Show[Plot3D[{Plane[x,y],Ellipsoid1[x,y],Ellipsoid2[x,y]},{x,-5,5},{y,-5,5},BoxRatios{1,1,1},AxesLabelAutomatic,PlotRangeFull,Lighting"Neutral"],ParametricPlot3D[{-t-2,2t+1,-2t/3-3},{t,-5,5}],Graphics3D[{PointSize[0.03],Point[{-2,1,-3},VertexColors{Red}]}]]
Out[]=
​