1. 9.2 – Parts of a Parabola

2. We have done/worked with many variations of a parabola The standard form of a parabola centered the center (h, k) is given by;

3. On a parabola, every point is a fixed distance from a point known as the focus and a fixed line known as the directrix

4. Standard Form Parabolas may be oriented in one of two ways; vertically or horizontally If a parabola is oriented vertically; – If p > 0, opens up; if p < 0, opens down – Focus is located at (h, k + p) – Directrix is the line from the equation y = k - p – Vertex; (h, k)

5. Example. If, find the focus and directrix.

7. Standard Form Parabolas may be oriented in one of two ways; vertically or horizontally If a parabola is oriented horizontally; – If p > 0, opens right; if p < 0, opens left – Focus is located at (h + p, k) – Directrix is the line from the equation x = h - p – Vertex; (h, k)

8. Example. If, find the focus and directrix.

10. Simplified Version If a parabola is center at the origin, then the equation for a parabola may be expressed simply as;, where p is the focus To find p, all we need are an x and y coordinate from the known parabola

11. Parabolic Mirrors A 3-d version of a parabola is better known as a “paraboloid” Form a parabolic mirror – Searchlights – Car lights – Telescopes – Satellites

12. Idea; light source (or similar) is placed at the focus, so that the light may be projected in an efficient/defined manner – Early lights vs later lights

13. Example. A light designer is charged with a new large light for search purposes. The light has a diameter of 10 feet, and a depth of 18 inches. How far from the vertex should the point of light be positioned?

14. Example. A certain brand of spotlight is made using a radius of 8 feet, and a depth of 2 feet for the shape of the paraboloid. In order to have the brightest/most concentrated light, how far from the vertex should the bulb be placed?

15. Assignment Pg. 718 1, 2, 7, 8 37-41 odd 55, 56