I am researching about Efimov's theorem, to illustrate what is being worked I need graphs this:

![image.png](/image?hash=87a1305e44ab3f0cf257ec821f8528ab5b9254be0087880cd9e2e031b46b6cd5)

the elliptical cylinder must have as its center (x,-1/3,0), in this way the cylinder must be parallel to the x axis. Where the planes are tangent to the cylinder and seen in the yz-plane, we have something like this

![image.png](/image?hash=26622e9d52136acaf19dc171bb12bf6bcfdfafb67114db584df5d071dbdb97e4)

I'm aware that I do not know much about making graphics in Latex but I have tried Asymptote and Tikz but I have not achieved anything, I would appreciate someone to help me. 
My attempt I did it in http://asymptote.ualberta.ca/ :
```
settings.render = 8;
size(10cm, 0);
import three;
import solids;
currentprojection = orthographic(2,0.5,1);

draw(unitsphere, gray + opacity(0.7));

triple v=(-1/2,-1,0);
real r=0.25;
real h=3;
triple axis=X+Y;

surface cylinder=shift(v)*align(unit(axis))*scale(r,r,h)*unitcylinder;
draw(cylinder,green,render(merge=true));

revolution r=cylinder(v,r,h,axis);
draw(surface(r),green,render(merge=true));
```
**Output**

![image.png](/image?hash=4d6e8c99a32e47833a43301552405a299926370230cdb27f5f499d506390f14b)