Question 1149939
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Minor axis is 8 units --- hence, the minor semi-axis is b= 8/2 = 4 units.


Eccentricity c= 3 --- hence, 

    c^2 = a^2 - b^2  ===>  a^2 = c^2 + b^2 = 3^2 + 4^2 = 25  ===> a = {{{sqrt(25)}}} = 5, where "a" is the major semi-axis.


Since minor axis is vertical, the ellipse  "is wider than tall"  and  "a"  goes with x-term,  while  "b"  goes with y-terms.


Taking into account the center's position, the standard form equation of ellipse is


    {{{(x-1)^2/5^2}}} + {{{(y-1)^2/4^2}}} = 1.    <U>ANSWER</U>
</pre>

Solved.


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For associated lessons, see 

&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>".



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.