Find the equation of an ellipse

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How can one find the eq. of an ellipse given that the foci are (-2,0) and (2,0) and that the directrices are x=-8 and x=8?
 
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What have you done with this problem? You need to show your work.
 
the ratio of distance to its focus to the distance to the corresponding directrix is a constant. even in the case of two foci, as in the ellipse, applying this on a single focus-directrix combination is the whole conic section.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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