Paraboline

Parabola is the locus of equi-distant point to a given point and a line. Now, what would happen if the line is changed to a segment of line? The a and b are the parameters to change the size and position the line segment. The c is the parameter to change the position of the given point C. The curve consists of three parts. On the left (blue), try to move the point H to the left and right. See what is going on. On the middle (red), try to move the point D to the left and right. See what is going on. On the right (green), try to move the point F to the left and right. See what is going on.