Visible and Invisible Intersections in the Cartesian Plane

Initializing live version
Download to Desktop

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




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.