Question 1087920
.<pre>
{{{x^2 + 9y^2}}} = {{{36}}}  is equivalent to  {{{x^2/36}}} + {{{y^2/4}}} = {{{1}}}


The center is at (0,0), the origin of the coordinate center.

The major axis is along the x-axis, while the minor axis is along the y-axis.

The major axis is  a = 6 = {{{sqrt(36)}}} units long.

The minor axis is  b = 2 = {{{sqrt(4)}}} units long.

The vertices are (6,0) and (-6,0), while the co-vertices are (0,2) and (0,-2).

The linear eccentricity is {{{c}}} = {{{sqrt(a^2 - b^2)}}} = {{{sqrt(6^2 - 2^2)}}} = {{{sqrt(32)}}} = {{{4*sqrt(2)}}}.

The foci of the ellipse are  ({{{-4*sqrt(2)}}},{{{0}}})  and  ({{{4*sqrt(2)}}},{{{0}}}).

</pre><TABLE> 
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  <TD> 

{{{graph( 500, 250, -10.25, 10.25, -5.5, 5.5,
          2*sqrt(1-(x^2/36)),
         -2*sqrt(1-(x^2/36))
)}}}


<B>Figure</B>. Ellipse {{{x2/36}}} + {{{y^2/4}}} = 1

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  </TR>
</TABLE>

See the lessons 

&nbsp;&nbsp;&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;&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;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-elements-of-an-ellipse-given-by-its-standard-eqn.lesson>Identify elements of an ellipse given by its standard equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-a-standard-equation-of-an-ellipse-given-by-its-elements.lesson>Find the standard equation of an ellipse given by its elements</A>

in this site.



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>".