Ellipses and hyperbolas by means of perpendicular bisectors

On a sheet of paper draw a circle and name its center "F_1". Then pick a point and call it F_2. Fold the paper so that F_2 meet the circumference at least 50 times (25 points and their opposite through the diameter): What do you get if the distance between F_1 and F_2 is less than the circle radius? What do you get if the distance between F_1 and F_2 is greater than the circle radius? What do you get if the distance between F_1 and F_2 is equal than the circle radius? By the way, did you notice the relation between the circle radius and the addition or the difference between the highlighted distances?

 

Omar G. Monteagudo

 
Resource Type
Activity
Tags
bisectors  ellipse  ellipses  folding  hyperbolas  mean  paper  perpendicular 
Target Group (Age)
15 – 18
Language
English (United States)
 
 
GeoGebra version
4.2
Views
1073
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