# Visible and Invisible Intersections in the Cartesian Plane

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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

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"Visible and Invisible Intersections in the Cartesian Plane"

http://demonstrations.wolfram.com/VisibleAndInvisibleIntersectionsInTheCartesianPlane/

Wolfram Demonstrations Project

Published: May 29 2018