Conic Section
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A
conic section
is the curve obtained by the intersection of a plane and a cone (a conic surface).
These are:
circle
- cutting perpendicular to the axis of symmetry of the cone
ellipse
- cutting at an angle less than the slope angle.
parabola
- cutting at an angle equal to the slope angle
hyperbola
- cutting at an angle greater than the slope angle
Image courtesy of the wiki commons.
There are some degenerate cases i.e. when the cutting plane passes through the apex of the cone:
point - a degenerate
circle
(or
ellipse
)
line - a degenerate
parabola
intersecting lines - a degenerate
hyperbola
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