The foci of a certain ellipse are at $(3,10 + \sqrt{105})$ and $(3,10 - \sqrt{105}).$  The endpoints of one of the axes are $(-5,10)$ and $(11,10).$  Find the semi-major axis.
Question:
The foci of a certain ellipse are at $(3,10 + \sqrt{105})$ and $(3,10 - \sqrt{105}).$  The endpoints of one of the axes are $(-5,10)$ and $(11,10).$  Find the semi-major axis.
Answer:
Let's think step by step.

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The foci of a certain ellipse are at $(3,10 + \sqrt{105})$ and $(3,10 - \sqrt{105}).$  The endpoints of one of the axes are $(-5,10)$ and $(11,10).$  Find the semi-major axis.
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