Shape of hyperbola
Steps:
1. On a wax paper draw a circle with center O
2. Take point A outside the circle.
3. Fold the paper so that the point А is on the circumference of the circle O.
4. Repeat the step 3 for various positions of A on the circle.
5. Which shape can you see?
Geogebra construction:
Folding a paper so that point A is on the circumference means drawing the perpendicular bisector of point A and and a point on the circumference.
See the construction below.
Is there any relation of points A and O with focuses?
What can you see if point A is near (far from) the circumference?