Geometricus Geometriorum (HP I, philosophical stone)

Geometry Level 4

\[ \frac{(x - 2017)^2}{576} + \frac{(y - 2016)^2}{625} = 1\]

Given the ellipse above, let

  • the distance between the foci of this ellipse be \(a\);
  • the sum of the distances from the point \(\left(2017 + 24\cos \dfrac{\pi}{4}, \ 2016 + 25\sin \dfrac{\pi}{4} \right)\) to the foci be \(b\).

Find \(a + b\).

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