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Conic Section for the Ellipse

  1. Apr 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the equation for the conic ellipse with vertices (-2,-5) (-2, 4) and foci (-2,-4) (-2,3)

    2. Relevant equations

    I want to make sure I am solving the problem correctly

    3. The attempt at a solution

    (x+2)^2/8 + (y+0.5)^2/20.25 =1
     
  2. jcsd
  3. Apr 25, 2013 #2

    symbolipoint

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    Here is some help.

    Standard equation for the ellipse you describe begins this way:
    (x-h)^2/b^2+(y-k)^2/a^2=1,
    and a is the semi-major axis length, and a>b.


    You gave focus points which are on the line, x=-2, and so consistant with the given major axis being vertical. Checking the vertices you find the value for a is |-5-(4)|*(1/2)=4.5,
    a=4.5

    You also find that based on the foci, the center of your ellipse is at x=-2 and y=(-4+3)*(1/2)=-(1/2); or the point for center is (-2, -1/2).


    There is a fairly well known relationship between a, c, and the minor axis length b. I leave finding this and the rest of the work to you. A review from a college algebra or intermediate algebra textbook will be very helpful. Give a try first before more help is given - if any needed.

    Checking your results again, it seems you mostly or entirely have the right idea; your center point reads correctly in your equation, at least.
     
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