Hyperbola FINAL Assign. 2
- Author:
- Alec Contreras
How to make a hyperbola
1. Select a circle with center through point, with origin A
2. Select a point in the circle C
3. Select a focal point D, along the outside of the circle
4. Select a perpendicular Bisector between Point D and Point C on the circle and it will yield you the fold, line a
5. Select a line b, running through points A and C
6. Select to move so that you could make an intersection between lines a and b
7. Find the intersection between lines a and b and label it E
8. On point E turn on the trace and add color to it
9. Select point C on the circle and on object properties turn on the animation so that point E will trace the hyperbola
Why this is a hyperbola
A hyperbola is defined as the locus of points where the absolute value of the difference of the distances to the two foci is a constant equal whose distance is doubled [2a], which refers to the distances between two points.
-In our hyperbola our two focus points are point D and A.
- In order to show that there's an absolute value relationship with the locus or the shape of the graph we notice point E.
Point E traces in red and it demonstrates that the distances share the same proportion in terms of size, length and appearance. Therefore the tracing of both lines yields a reflection for each line, with an asymptote between the traced lines.
-The distance between the focus points is seen in the relationship of '2a' because we constructed a perpendicular bisector (line a)which shows that the distances between the points are equidistant.
It's also worth noting that the actual hyperbola bisects points A and D.