GEOMETRIC CONSTRUCTION OF CONIC SECTIONS
Section: Geometry
 
1. THE PARABOLA
Now we are ready to draw the parabola. We need to move point P along the straight line which we can do by using the arrows, as we get a better drawing this way. 

 

1.- Move point P and see how the trace of the movement contains a parabola.
This time point P cannot move anywhere on the plane. It can only move along the straight line.

2.-  Use the arrows to change the values of 'move P' and you will see how the line moves nearer or further away to point Q. Clear the window and draw another parabola for a different value.

3.- What happens when point Q is on the the straight line?

 
2. THE HYPERBOLA
The situation is similar to the one above but this time the movement of P is restricted to the circumference of a circle. As the point moves around the circle we can see that its trace of straight lines contains a hyperbola. Note that point Q is located outside the circle. 
 

1.- Move point P and watch how the trace of the movement contains a hyperbola.

The Init button will take you back to the start.

2.- If you change the value of the radius you will see that the circle becomes bigger or smaller. Clear the window and draw another hyperbola with a radius of a different value.
 

 
3. THE ELLIPSE
The situation is similar to the one above as the movement of P is also restricted to the circumference of a circle. As the point moves around the circle we can see that its trace of straight lines contains an ellipse. Note that this time point Q is inside the circle.

1.- Move point P and watch how the trace of the movement contains an ellipse.


2.- Change the value of the radius and watch how the circle becomes bigger or smaller. Clear the window and draw another ellipse.


3.- Find out whether the shape of an ellipse is rounder when P is closer or further away to Q. What role does the radius of the circle play in this?
 
 
     
           
  Agustín Muñoz Núñez
 
Spanish Ministry of Education. Year 2001
 
 

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