Algebraic Curve Intersection Explorer

Live Script finding intersections of affine algebraic curves.

An affine algebraic curve is a planar curve described by a polynomial equation in two variables x and y. The intersections of two such curves may be found analytically with solve or numerically with vpasolve or by solving a resultant polynomial equation for a root vector X or Y and then calculating the corresponding vectors Y or X. The resultant equation can be solved with solve, vpasolve, or roots, the latter designed to solve single variable polynomial equations using the polynomial coefficients.

This educational Live Script illustrates these methods to find intersections of lines, parabolas, hyperbolas, ellipses, and other curves. The script may interest students and instructors in physics and other STEM fields. 'Try this' suggestions and 'Challenges' are included for further exploration. For additional educational Live Scripts by the author, see Ref[1].