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Restricting Domain and Range in broken conics

  1. Mar 22, 2009 #1
    1. The problem statement, all variables and given/known data
    How do you know whether you restrict the domain or range with a horizontal ellipse ?


    2. Relevant equations
    x^2/49 +y^2/10=1


    3. The attempt at a solution
     
  2. jcsd
  3. Mar 22, 2009 #2

    HallsofIvy

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    Since y2 is never negative, x will be largest when y= 0. And when y= 0, [itex]x^2/49= 1[/itex], [itex]x^2= 49[/itex], [itex]x= \pm 7[/itex]. [itex]-7\le x\le 7[/itex]. Similarly, if x= 0 [itex]y^2/10= 1[/itex] so [itex]y= \pm\sqrt{10}[/itex]. If x is not zero, [itex]y^2[/itex] is smaller than 10 so [itex]-\sqrt{10}\le y\le\sqrt{10}[/itex].
     
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