Assignment #6- Parabola
The purpose of this assignment is to construct a parabola. A parabola is the set of points equidistant from a line, called the directrix, and a fixed point, called the focus.We assume that the focus is not on the line. Given the focus, pt. F, and the directrix, we can construct a parabola. In the following construction x is any point on the directrix.. For this particular animation the x-axis is the directrix and the range of x has been limited. Tracing the animation of point Y, that is the intersection of lines d and h, gives the following parabola:
We can confirm that this construction is in fact a parabola since segments FY and YX are always the same length during the animation of point X. Therefore point Y is always equidistant from the directrix, the x axis, and the focus, point F.
Again using the same construction but tracing the line tangent to point Y. We obtain the following construction of the envelope of the parabola. Click here to see this animation in GSP.
Now using the locus command to construct the parabola from point Y and the animated point on the directrix, point X gives:
Again using the locus command to construct the parabola and its envelope from the line tangent to point Y and the animated point X gives the following construction. Click here to see this construction in GSP.