# A Planar Cut Through an Ellipsoid

Geometry Level 5

An ellipsoid with center $$(0,0,0)$$ and semi-axes of 10, 15, and 30, along the $$x, y,$$ and $$z$$ directions, respectively, is cut by a plane whose equation is $$x + 3y + 2z = 40$$. The intersection of the ellipsoid and the plane is an ellipse. Find its area.

This problem is original.

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