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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
and the solution as it should be.
(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 = 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
+ = 1, or, equivalently,
+ = 1.
It is your final answer.
Solved.
Now you have not only right equation, but the full and correct logical chain of arguments which leads to the equation.