If we cut a cone with a plane parallel to its base we get a circle. Now if we tilt the plane we get various curves like ellipses, parabolas and hyperbolas. Now my question is that, can we transform our Cartesian coordinate system to another where the effect of tilting the plane is undone. I mean how can I transform the coordinates along with tilting plane to get a circle always.
2026-04-12 01:19:07.1775956747
Cutting a cone with a plane and then tilting the plane
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I guess this question comes out by pure curiosity. For what matters yes you can do it, you can imagine to rotate the cone along with the plane so that the plane will be parallel to the base. Bare in mind that if you take a class of linear algebra this question will look silly to you, and going beyond that you will see an actual definition of conics which is not the one you probably encountered in an High school.