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Integrals, Rate of Change and Ellipses

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Please help with 7C, 10 and 12
7. Find the integral...
10. A beacon on a lighthouse 2000 m away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 m from P? (7 points)

12. Find the rectangle of maximum area that can be inscribed in the ellipse
?+?=1

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Integrals, rate of change and ellipses are investigated and discussed in the solution. The solution is detailed and well presented.

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7C) Let
Then, put secx=t which gives secx tanx dx=dt. Using tan2x=sec2x-1, we get

10.

Let B is beacon and the angle at which it is seen from ...

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