1 / 12

Chapter 8

Chapter 8. 8-1 : parabolas 8-2 : ellipse 8-3 : hyperbolas 8-4 : translating and rotating conics 8-5 : writing conics in polar form 8-6 : 3-D coordinate system (plotting points, planes, vectors) . Section 8-1. the conic sections definition of parabola

siran
Download Presentation

Chapter 8

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 8 • 8-1 : parabolas • 8-2 : ellipse • 8-3 : hyperbolas • 8-4 : translating and rotating conics • 8-5 : writing conics in polar form • 8-6 : 3-D coordinate system (plotting points, planes, vectors)

  2. Section 8-1 • the conic sections • definition of parabola • standard form of the equation of a parabola • translating a parabola • graphing a parabola • convert from general form to standard form • reflective property of parabolas

  3. Parabola: the set of all points equidistant from a particular line (the directrix) and a particular point (the focus). focus directrix

  4. Parabola: the set of all points equidistant from a particular line (the directrix) and a particular point (the focus). focus directrix

  5. Vertex: the vertex is midway between the focus and the directrix focus vertex directrix

  6. Vertex: the vertex is midway between the focus and the directrix Focal Length: the distance from the focus to the vertex, denoted with the letter p focus p { vertex directrix

  7. Standard Form of a ParabolaVertex at (0 , 0) Focus at (0 , p) 4p p p Focal length = p Focal width = Directrix at y = – p if p is negative, the graph flips over the x-axis

  8. Standard Form of a ParabolaVertex at (0 , 0) p p 4p Focus at (p , 0) Focal length = p Focal width = Directrix at x = – p If the value of p is negative, the graph opens to the left (flips over the y-axis)

  9. Translating a Parabola • if the parabola has a vertex of (h , k) the two equations change into: • notice that h is always with x and k is always with y • the focus and directrix will adjust accordingly

  10. Sketching the Graph of a Parabola • convert the equation into standard form, if necessary • find and plot the vertex • decide which way the graph opens (based on p and which variable is squared) • add the focus and directrix to your graph • use the focal width to find two other points (these will give the parabola’s width) • graph the rest of the parabola

  11. Convert Into Standard Form • to convert from general form into standard form you must use “complete the square”

  12. Reflective Properties of Parabolas • if a parabola is rotated to create a 3-D version it is called a “paraboloid of revelolution” • there are many examples of parabolic reflectors in use today involving sound, light, radio and electromagnetic waves

More Related