Question 1169049
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The center (2,-3) and focus (2,3) are on the same vertical line, so the major axis is vertical.<br>
General equation:<br>
{{{(x-h)^2/b^2+(y-k)^2/a^2 = 1}}}<br>
The center is (h,k); a is the semi-major axis and b is the semi-minor axis.<br>
The center (h,k) is (2,-3); the major axis is 16, so the semi-major axis is a=8.<br>
{{{(x-2)^2/b^2+(y+3)^2/8^2 = 1}}}<br>
The distance from the center to the focus is c, where a, b, and c are related by {{{c^2=a^2+b^2}}}<br>
In this problem, c is the distance from (2,-3) to (2,3).<br>
So you know a and c; so you can calculate b.  Then you will have everything you need to write the equation.<br>