1
$\begingroup$

I have a cone and a plane myQ = x - 4 y + z + 4 == 0;. How can I draw the intersection of the cone and the plane myQ?

  Clear["Global`*"]
pA = {2, 3, 0};
myP = 2 x + y + 2 z - 1 == 0;
reg1 = ImplicitRegion[x \[Minus] 4  y + z + 4 == 0, {x, y, z}];
pH = RegionNearest[ImplicitRegion[myP, {x, y, z}]]@pA;
d = Sqrt[5^2 - EuclideanDistance[pA, pH]];
reg2 = Cone[{pA, pH}, d];
r2 = RegionIntersection[reg1, reg2];
Graphics3D[{Gray, Opacity[0.5], reg2}, Boxed -> False]

Show[Region[Style[r2, Cyan]]]

enter image description here

enter image description here

Show[Region[Style[reg1, Red]], Region[Style[reg2, Blue]]]

enter image description here

$\endgroup$
0

1 Answer 1

2
$\begingroup$

Set PlotRange in Region.

Show[Region[Style[reg1, Opacity[.3], Red], PlotRange -> 8], 
 Region[Style[reg2, Opacity[.2], Blue]], Region[Style[r2, Cyan]]]

enter image description here

  • Add BoundaryStyle.
Show[Region[Style[reg1, Opacity[.3], Red], PlotRange -> 8], 
 Region[Style[reg2, Opacity[.2], Blue]], 
 RegionPlot3D[DiscretizeRegion@r2, 
  BoundaryStyle -> Directive@{Dashed, Thick}, PlotStyle -> Cyan]]

enter image description here

$\endgroup$
1
  • $\begingroup$ Can I get the equation of the parabol is intersection of the cone and the plane? $\endgroup$ Commented Mar 23 at 3:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.