To do and explore: The image is constructed the following way; The point P runs freely on the blue line. The line L1 is perpendicular to the segment FP.
If you doubleclick the immage, you can use the trace tool and click on the line L1. Use the animation spring on the point P. Now a set of lines will be drawn, and the envelope of those lines is a parabola.
To do and explore: This immage is formed in the same way as the one above with the difference that the blue line is replaced by a circle. Use trace and animation the same way as before. The envelope this time will be an ellipse.
Now, press the update button among the web browser tools. Move F1 just outside the circle. Use trace and animation once again. This time you will get a hyperbola.
Note that if the point F1 is inside the circle, we get an ellipse and if F1 is outside the circle we get a hyperbola. If we regard the line in the upper immage as a circle with infinit radius, then F1 can be seen as a point inside and outside this circle. The parabola is the limit between the ellipse and the hyperbola.