Question 1137157
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            To solve this problem,  the correct logical chain of arguments should be build  (and presented)  in a right way.


            I do not see this correct logical chain in the solution of the other tutor,  so I came to present here this logical chain


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and the solution &nbsp;<U>as it should be</U>.



<pre>
(1)  Since the center and the vertex have the same y-coordinates  y= 5, it means that the corresponding semi-axis is horizontal 

     and has the length of  9 - (-2) = 9 + 2 = 11 units.

     Thus we have horizontal semi-axis of 11 units long.



(2)  Now, the minor semi-axis is  {{{10/2}}} = 5 units long, as it follows from the given part.

     Since this length is different from 11 units, it means that the minor semi-axis is vertical, parallel to y-axis.


     It also means that 11-unit semi-axis is the major-semi-axis.

     

(3)  Now we have the full information, geometrically describing the given ellipse and, hence, we are ready to write the equation


         {{{(x-(-2))^2/11^2}}} + {{{(y-5)^2/5^2}}} = 1,    or,  equivalently,


         {{{(x+2)^2/11^2}}} + {{{(y-5)^2/5^2}}} = 1.


     It is your final answer.
</pre>

Solved.


Now you have not only right equation, but the full and correct logical chain of arguments which leads to the equation.