Ask AI: how do you make two conic shapes have more than 4 intersections

It is generally not possible for two conic sections to have more than 4 intersection points. If you graph two conic sections on a Cartesian plane, the maximum number of times they can intersect is 4 points. This is because conic sections are described by quadratic equations, and when you solve for the intersection(s) of two conic sections, you get a system of two quadratic equations. The maximum number of solutions to a system of two quadratic equations is 4. However, you can have multiple conic sections that intersect at more than 4 points combined, but no two of them will have more than 4 intersections with each other. An example would be having multiple circles that share a common point, or multiple ellipses that intersect each other at various points.