Oh thank you. But then how do you sketch the locus without finding the equation? As in how do you know it lies strictly in the first quadrant? And after finding 2a, how do you find 2b without the equation?
You don't know everything. Some things you have to infer.
2a is of course, given.
But the distance between the two foci is 2ae. Recall that SS' = 2ae
You are given the foci in the question.
Since the foci are at (1,3) and (9,3), the focal length is 4.
Hence 4 = ae
So e=4/5
Then you can use b^2=a^2(1-e^2) to find the length of the minor axis.
Note also that the ellipse's centre is also at (5,3)
Given the centre, and the length of the major and minor axes, you should be able to sketch the ellipse.