Question 1092965
.
<pre>
Notice that the center and the vertex lie in one vertical line x = 1.

Hence, the major axis is vertical line x = 1 parallel to y-axis.


Next, the major semi-axis length is the distance from the ellipse center to the vertex, i.e. 7-4 = 3 units.

Further, since the eccentricity is {{{2/3}}}, the minor semi-axis is  {{{(2/3)*3}}} = 2 units,  and the ellipse is taller than wide.


Thus the equation of the ellipse is 

{{{(x-1)^2/2^2}}}} + {{{(y-4)^2/3^2}}} = 1.



{{{graph( 330, 300, -4.5, 6.5, -8.5, 1.5,
          -4 + 3*sqrt(1-((x-1)^2/4)),
          -4 - 3*sqrt(1-((x-1)^2/4))
)}}}


&nbsp;&nbsp;&nbsp;&nbsp;Ellipse {{{(x-1)^2/4}}} + {{{(y-4)^2/9}}} = 1
</pre>

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>".



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.




============================
Dear "students" !


Today is a special day.

Today I solved &nbsp;16 &nbsp;problems for you and got back &nbsp;0 &nbsp;(zero, &nbsp;ZERO) &nbsp;"thanks" &nbsp;from you.


It is the absolute record&nbsp;! 
&nbsp;&nbsp;&nbsp;&nbsp;It is just out of limits of my understanding &nbsp;!
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I never saw it before &nbsp;!


Thank you very much and wish you to think: &nbsp;&nbsp;<U>WHO ARE YOU . . . </U>