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24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
January 1, 2020
Solved

Cone, plane, ellipse

  • January 1, 2020
  • 2 replies
  • 5661 views

I know a and b of an ellipse. What is the value alpha of a circular cone?

Cone.png

Best answer by ptc-5737066

Yes,

N.png

here is example when a=15, b=8 and alpha=30 degree...

N2.png

..and when alpha changes to 40 degree

Observe that auxiliary view is normal to cutting plane and does not show real cone angle.

2 replies

P
ptc-57370661-Visitor
1-Visitor
January 2, 2020

a & b are not sufficient to define alpha.

No mather what alpha you have, you can allways slice cone to obtain ellipse with dimmensions a & b.

/Avdo

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    January 2, 2020

    Thanks!

    For a of a circular cone too?

    P
    ptc-57370661-Visitor
    1-Visitor
    January 3, 2020

    Yes!

    When Dandelin spheres touch eachother both focuses and ellipse center melt into touch point onto axe and ellipse becommes circle.

    Since that no focus points nor ellipse center can coincident with axis.

    Axis is allways intersecting the line between two focuses splitting it in one longer and one shorter part. 

    -
    -MFra-21-Topaz II
    21-Topaz II
    January 4, 2020

    Hi,

    With the use of analytical geometry and with the data available, this is all you can do:

    Risposta a V. O..jpg

    Happy New Year.

    F. M.

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