Question 1126654
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1.    You correctly found one of many possible solutions.


2.    There are MANY possible solutions.    They are


                    {{{x^2/a^2}}} + {{{y^2/b^2}}} = 1    


            with  5 = {{{sqrt(a^2 - b^2)}}}   and with not necessary integers  "a"   and   "b".



3.    For ellipses,  there are three major types/forms of equations:


      a)    a canonical equation.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See the lesson &nbsp;&nbsp;<A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-definition--canonical-equation--characteristic-points-and-elements.lesson>Ellipse definition, canonical equation, characteristic points and elements</A> &nbsp;&nbsp;in this site;


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b)  &nbsp;&nbsp;the standard form equation.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See the lesson &nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Standard-equation-of-an-ellipse.lesson>Standard equation of an ellipse</A> &nbsp;&nbsp;in this site;


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c)  &nbsp;&nbsp;the general form equation.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See the lesson &nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/General-equation-of-an-ellipse.lesson>General equation of an ellipse</A> &nbsp;&nbsp;in this site.


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Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Conic sections: Ellipses. Definition, major elements and properties. Solved problems</U>".



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.