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A plane passing through the apex of a cone gives, in the general case,

  • A.two intersecting straight lines
  • B.a circle of vanishing radius
  • C.a parabola through the apex
  • D.an ellipse tangent to the base

Answer: A

Correct answer: two intersecting straight lines

A plane through the apex meets the surface in generators rather than in a curve. In the general case it cuts two of them, giving a pair of straight lines crossing at the apex; tangential to the cone it gives one; and passing through the apex without entering the cone, only the apex itself. These are the degenerate conics.

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