# Constructing a Parabola

## Goal:

Our goal is to find the locus of points that is equidistant from a line and a point.
Below, we have a line at f(x) = -1 and a point at (0 , 1).
A circle centered at point A has been created with a radius determined by slider d.

## Directions

1) The locus of points a certain distance d from the line is a new line g(x) = f(x) + d. Type this new function, then move the slider to see where g(x) moves.
2) Move the slider so that there are 2 intersection points for g(x) and the circle. Create 2 points of intersection, B and C.
3) Create point D=(x(B) , f(0)).
4) Make line segments AB and BD.

Using the slider, what do you notice about AB and BD?

## Directions (Part 2)

5) Create point E = (x(C) , f(0))
6) Right click on points D and E and choose "Trace on"

What happens when you move the slider?

After completing this construction, how would you define a parabola?

## Extension

Try changing the location of A and f(x).