1729 is interesting!

Geometry Level 5

The above diagram shows an ellipse \((E):\) \[\frac{(x-17)^2}{17}+\frac{(y-29)^2}{29}=1729\]Suppose \(S_1,S_2,S_3\) and \(S_4\) represent the area of 1, 2, 3 and 4 marked on the diagram. Determine the value of \(M=S_1+S_3-(S_2+S_4)\).

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