A popular curve shown in introductory maths textbooks, seems like a circle.
But it is actually a different curve. This paper discusses some elementary
approaches to identify the geometric object, including novel technological
means by using GeoGebra. We demonstrate two ways to refute the false
impression, two suggestions to find a correct conjecture, and four ways to
confirm the result by proving it rigorously.
All of the discussed approaches can be introduced in classrooms at various
levels from middle school to high school.