Using focus-directrix graph paper, sketch a parabola that has a horizontal directrix four units above the focus, which is at $(0, 0)$. You can get focus-directrix paper on the Lesson 10.1.3 Resource Page.

1. Write an expression for the distance from the focus to any point $(x, y)$ on the parabola.

   Answer (a):

   $\sqrt{x^2+y^2}$

2. Write an expression for the distance from the directrix to any point $(x, y)$ on the parabola.

   Hint (b):

   Notice that the closest point on the directrix is going to have the same $x$-value.

3. If all of the points on a parabola are equidistant from the focus and directrix, use your expressions from parts (a) and (b) to write an equation for the parabola.