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Equation of Ellipse

  1. Feb 19, 2009 #1
    If (5,12) and (24,7) are the focii of a conic passing through the origin, then find the eccentricity of the conic

    Attempt:

    Found the centre as (h,k), midpoint of the given points. (x-h)^2/a^2+(y-k)^2/b^2=1 i put x=0 and y=0 as it passes through the origin. from the equation e^2=1-(b^2/a^2) i got a relation between a and b. distance between the two given points equals 2a*e thereby giving the second relation, manipulating both the equations, i got a quadratic in e which i solved but it became tedious and finally i got the wrong answer.

    Help would be appreciated!
     
  2. jcsd
  3. Feb 19, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi hellboydvd ! Welcome to PF! :smile:

    Hint: what is the sum of the distances of the foci (not focii!) from the origin, in terms of a b and e? :wink:
     
  4. Feb 19, 2009 #3

    HallsofIvy

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    But notice that the form (x-h)^2/a^2+(y-k)^2/b^2=1 is only valid for an ellipse with axes parallel to the coordinate axes. Fortunately, you don't need the equation of the ellipse to do this problem.
     
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