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Every plane section of a sphere, whatever its position, is

  • A.a parabola for planes not through the centre
  • B.a circle
  • C.an ellipse unless the plane passes through the centre
  • D.a circle only when the plane passes through the centre

Answer: B

The surface is equidistant from the centre in every direction, so any plane cuts it in a curve of constant radius about the foot of the perpendicular from the centre. Only the radius of that circle changes with the plane's distance from the centre.

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