Question 1159590
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The length of the semi-major axis is the distance from the center to a vertex.  The center is (1,4); one vertex is (1,9); the length of the semi-major axis is 5, and it is in the y direction.<br>
Minor axis length 6 means length of semi-minor axis is 3.  Since the major axis is in the y direction, the minor axis is in the x direction.<br>
The general equation of an ellipse with center (h,k), semi-major axis a in the y direction and semi-minor axis b in the x direction is<br>
{{{(x-h)^2/b^2+(y-k)^2/a^2 = 1}}}<br>
Plug in the numbers we were given or have found:<br>
{{{(x-1)^2/3^2+(y-4)^2/5^2 = 1}}}<br>
{{{(x-1)^2/9+(y-4)^2/25 = 1}}}<br>