the.com/conic section
what you get when a plane rudely interrupts a cone's personal space.
means the curve formed by slicing a cone with a flat plane: circle, ellipse, parabola, or hyperbola, depending on the angle.
from studied by ancient greek geometers, most famously apollonius of perga around 200 bce, who wrote an entire treatise just cataloguing the ways to cut a cone.
same familycircle and hyperbola are cousins, not opposites
planetary orbitskepler proved orbits trace ellipses, not circles
one equationall four curves solve one quadratic equation
double conehyperbolas need both nappes of the cone