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Question 56426: Hope you can help me
"What degenerate form or forms of the parabola cannot be obtained from the intersection of a plane and a double napped cone? Describe how to obtain this (or these). Use a diagram to support your answer."
Thanks in advanced
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! "What degenerate form or forms of the parabola cannot be obtained from the intersection of a plane and a double napped cone? Describe how to obtain this (or these). Use a diagram to support your answer."
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Think of an icecream cone sitting on a table with
the circular opening on the table and the tip above.
Think of a second cone that is tip-to-tip with the
1st cone i,e, perched upside down on the 1st cone.
The sides of these two cones form an X shape.
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Degenerate forms:
A plane perpendicular to the table and passing thru the
tips of both cones will intersect the cones in an X pattern.
This it the degenerate form of the hyperbolic curves you would
get if the plane is perpendicular to the table but does not
pass thru the tips.
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A plane parallel to the table and passing thru the pt.
at which the tips meet forms a point.
This is the degenerate form of the circle curve you would
get if the plane is parallel to the table and intersects
a cone but not at the tip.
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A plane containing the edge of the two cones forms a line.
This is the degenerate form of the parabolic shapes formed
by a plane passing thru the cones parallel to an edge.
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Cheers,
Stan H.
the edge w
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