Visible and Invisible Intersections in the Cartesian Plane
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The circle and the straight line are plotted on the Cartesian plane. Their two intersections and , shown as black points, represent solutions of the simultaneous equations. But suppose the value of is such that the two curves do not intersect? There are still two perfectly good algebraic solutions of the simultaneous equations: , but these now involve complex numbers. You can imagine that the two intersections are now invisible.
Contributed by: S. M. Blinder (May 2018)
Open content licensed under CC BY-NC-SA
"Visible and Invisible Intersections in the Cartesian Plane"
Wolfram Demonstrations Project
Published: May 29 2018