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9.2 Parabola

9.2 Parabola. Hyperbola/Parabola Quiz: FRIDAY Concis Test: March 26. Parabola. A parabola is defined in terms of a fixed point, called the focus , and a fixed line, called the directrix .

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9.2 Parabola

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  1. 9.2 Parabola Hyperbola/Parabola Quiz: FRIDAY Concis Test: March 26

  2. Parabola • A parabola is defined in terms of a fixed point, called the focus, and a fixed line, called the directrix. • In a parabola, the distance from any point, P, on the parabola to the focus, F, is equal to the shortest distance from P to the directrix. • That is, PF = PD for any point, P, on the parabola.

  3. Standard Equation of a Parabola • Vertical directrix • p > 0: opens right • p < 0: opens left • You go left and right the value of p to get your focus and directrix. • Horizontal directrix • p > 0: opens up • p < 0: opens down • You go up and down the value of p to get your focus and directrix

  4. Something to keep in mind • The focus should always be “in” your curve. • The directrix should always be “outside” of your curve.

  5. Example: • Graph . Label the vertex, focus, and directrix.

  6. You Try: • Graph . Label the vertex, focus, and directrix.

  7. Example: • Write the standard equation of the parabola with its vertex at the origin and with the directrix y = 4. • Sketch a graph if you need to.

  8. You Try: • Write the standard equation of the parabola with its vertex at the origin and with the directrix x = -6. Next

  9. Horizontal Directrix Back F(0,p) y = -p

  10. Vertical Directrix x = -p Back F(p,0)

  11. 9.2 Continued Hyperbola/Parabola Quiz: FRIDAY! Conics Test: March 26

  12. Standard Equation of a Translated Parabola Horizontal Directrix Vertical Directrix

  13. Example: • Write the standard equation of the parabola with its focus at (-3,2) and with the directrix y = 4 • Sketch a graph if you need to.

  14. You Try: • Write the standard equation of the parabola with its focus at (-6,4) and with the directrix x = 2.

  15. Example: • Graph the parabola y2 – 8y + 8x + 8 = 0. Label the vertex, focus, and directrix.

  16. Graph:

  17. You Try: • Graph the parabola x2 – 6x + 6y + 18 = 0. Label the vertex, focus, and directrix.

  18. Graph:

  19. Practice • Parabola WS THIS IS A LOT: PRACTICE!

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