A parabola is the set of points equidistant from a line, called the directrix and a point, which is called the focus. In the link below to a parabola being made in GSP, the parabola will be the set of all the points which are equidistant from point A to the point moving along the segment BC and from A to the intersection of our perpendicular lines (this will be the point which we are tracing to make a parabola). That implies that those three points will always make an isosceles triangle.
In the next link, we will trace the line which is the perpendicular bisector to the segment containing A and the point moving on segment BC. This creates the tangent lines to the parabola we constructed before.