Question 1143600
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The standard form of the equation, with the major axis vertical, is<br>
{{{(x-h)^2/b^2+(y-k)^2/a^2 = 1}}}<br>
where the center is (h,k), a is the semi-major axis, and b is the semi-minor axis.<br>
The distance from the center to each focus is c, where c^2 = a^2=b^2.<br>
The distance between the two given foci is 8, so c is 4.<br>
The sum of the distances from any point on the ellipse to the two foci is 2a, so a is 7.<br>
That gives you all the information you need to write the equation.