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9.2 – Parts of a Parabola

9.2 – Parts of a Parabola . We have done/worked with many variations of a parabola The standard form of a parabola centered the center (h, k) is given by;. On a parabola, every point is a fixed distance from a point known as the focus and a fixed line known as the directrix.

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9.2 – Parts of a Parabola

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  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.

  6. 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.

  9. 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

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