Expert: Richard J. Raridon - 1/14/2010

Question
how do u get the definition of ellipses which is square root of (x+c)squared + (y-0)squared (end square root) + the square root of (x-c)squared +(y-0)squared (end square root) = 2a .... all the way too Xsquared/Asquared + Ysquared/Bsquared = 1

By the way you have to use the substitution property of Asquared= Bsquared + Csquared in there at some point

Answer
A figure satisfying the conditions (x-h)^2/a^2 +(y-k)^2/b^2 = 1 or
(y-k)^2/a^2 +(x-h)^2/b^2 = 1, when a not equal b, is defined as an ellipse.  I don't know whether you can get from there to what you have or not, assuming h and k = c and 0.  You certainly don't need a^2+b^2=c^2 which applies to right triangles.