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Find the area of the ellipse obtained from intersecting a plane with the normal vector n = i +3+k with a cylinder of radius 1

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Find the area of the ellipse obtained from intersecting a plane with the normal vector n = i +3+k with a cylinder of radius 1 and the axis parallel to the z-axis. Note that there are infinitely many such situations but only one answer. Use the surface area formula for double integrals

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