Question 1087976
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<pre>
From the condition:

The major axis (connecting foci) is the horizontal line y = 0, coinciding with x-axis.

The center of the ellipse is the midpoint between the foci, i.e. (2,0).

The focal distance is 2c = 4 - 0 = 4;  Hence, the distance from the center to each focus is c = {{{4/2}}} = 2.


Since the major axis length is 6, the major seni-axis is {{{6/2}}} = 3.


Then the minor semi-axis is  {{{b^2}}} = {{{a^2 - c^2}}} = {{{3^2 - 2^2}}} = 5.


Thus the standard form of the ellipse equation is

{{{(x-2)^2/3^2}}} + {{{y^2/5}}} = 1.
</pre>

Solved.


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>".