Equation and shape of the parabola

Author:
Mathguru
We can clearly see the graph of a parabola in red with focus at point A (blue) and directrix ‘a’ (green). Directrix ‘a’ is a line which passes through two points B and C. We can move the three points A, B and C. On moving any of the three points A, B and C we see that the size and position of the parabola gets altered
Questions to think about 1. Let us change the positions of the three points A, B and C and observe how the shape and position of the parabola gets altered. 2. Let us fix the position of point C and make it same as position of point A. What do we observe? Hint: make A and C = (2,2)