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A Planar Cut Through an Ellipsoid

An ellipsoid with center (0,0,0)(0,0,0) and semi-axes of lengths 10, 15, and 30 along the x,y,x, y, and zz directions, respectively, is cut by a plane whose equation is x+3y+2z=40 x + 3y + 2z = 40 .

The intersection of the ellipsoid and the plane is an ellipse.

Find its area.


This problem is original.

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