Question 1176728
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Check to see that you have entered the information correctly.  With the center at (3,3) and one focus at (2,6), the axes of the ellipse are not horizontal and vertical.<br>
To find the equation algebraically, you would have to determine the other focus (easy -- (4,0)) and then use the definition of an ellipse as the locus of points for which the sum of the distances from the two foci is a constant, with that constant being the length of the major axis:<br>
{{{sqrt((x-2)^2+(y-6)^2)+sqrt((x-4)^2+y^2)=12}}}<br>
Putting that in standard form would require some ugly algebra....<br>
Or you could go to wolframalpha.com and enter this in the question box:  "equation of ellipse with major axis 12, center (3,3), and focus (2,6)"<br>
But I suspect the problem is supposed to have different information than what you show....<br>