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Some problems with conic sections

  1. Dec 18, 2009 #1
    Here are some conic questions that am having problems with :

    1) The general form of a particular ellipse is show Below. If the conic is translated 2 units left and 1 unit down, determine the new general term.

    2x2+y2-2x+3y-9=0

    2) Find the equation of a hyperbola in standard form or general form, that has its centre at (-2, 5), one vertex at (-2, 10), and the slope of one of its asymptotes is 5/4 .

     
  2. jcsd
  3. Dec 18, 2009 #2

    rl.bhat

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    Re: Conics

    The standard equation of ellipse becomes
    (x - 1/2)^2/(47/8) + (y-3/2)^2/(47/4) = 1
     
  4. Dec 19, 2009 #3
    Re: Conics

    Whats the question?
     
  5. Dec 19, 2009 #4
    Re: Conics

    Sorry, i meant to ask if what i did is correct , or is there something am missing ?
     
  6. Dec 20, 2009 #5

    HallsofIvy

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    Re: Conics

    There is no need to convert to standard form. "Translating 2 units left" is exactly the same as adding 2 to x. "Translating one unit down" is exactly the same as subtracting 1 from y. Replace x by x+2 and y by y- 1.


    Rotating through an angle [itex]\theta[/itex] gives [itex]x'= x cos(\theta)+ y sin(\theta)[/itex], [itex]y'= x sin(\theta)- y cos(\theta)[/itex]. Replace x by [itex]x cos(\theta)+ y sin(\theta)[/itex], y by [itex]x sin(\theta)- y cos(\theta)[/itex]. [itex]\theta= arctan(5/4)[/itex].
     
  7. Dec 20, 2009 #6
    Re: Conics

    Thanks alot ! :D
    really appreciate it
     
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