How many points are needed?
It is known that distinct points are needed to uniquely determine a conic section (ellipse, parabola, hyperbola) in the plane. How many distinct points are needed to uniquely determine an arbitrary conic section in the three dimensional space ? You can assume that the given points are coplanar, and that no three of them are collinear.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The ellipse in 3D space still lies on a plane; the points are coplanar. This means that we can always rotate and shift the coordinate system to make the ellipse centered at the origin and lying on the plane z = 0 . This is equivalent to the ellipse in the x y plane so the same number of distinct points are required. Thus, the answer is 5 .