(EFOMM 2025) Área do hexágono gerado por pontos de uma elipse, uma hipérbole e uma circunferência

Consider the hyperbola 9y^2-16x^2-144=0 and take point A as its vertex on the positive y-axis and point E as its vertex on the negative y-axis. Take B and D, respectively, as the points with the highest and lowest y-coordinate values ​​in the geometric locus x^2+y^2-10x+9=0. Take C and F, respectively, as the points with the highest and lowest x-coordinate values ​​in the geometric locus 64x^2+121y^2-320x-1536=0. What is the area of ​​the convex polygon ABCDEF? #ita #ime #efomm