Parabola Given a focus and directrix
Use this applet to verify your answers on the worksheet given. You will need to move the slider for the directrix and move point F for the forcus or type F=(x,y) in the input bar, with x and y be the coordinated you want to use.
Questions:
1. How can you find the vertex of the parabola given the focus and directrix?
2. What can you say about the distance between the parabola and the focus or directrix at the vertex?
3. How does a related to the focus and directrix?
Write an equation for each parabola described below. (Vertex Form).
4. focus at (0, –2) and directrix x = 2.
5. focus (3,5) and directrix x=1
6. focus (5,-1) and directrix x=3
7. focus (4,-4) and directrix x=-6
8. focus (-3, 3 3/4) and directrix x= 4
9. vertex (-1, 5) and focus (3, 5).
10. vertex (-1.5, –2) and directrix x = –5.
More Questions:
11. How would our formula for finding the equation change if the directrix was y=n?
You can graph it or use GeoGebra to create this parabola, try a couple of different ones and make a conjecture.
12. Compare your conjecture with at least two other people in the class and see if agree with them. Document their conjecture and if you need to make adjustments to your conjecture note them below.