Question

Two cones are cut by a plane as shown, where the plane is perpendicular to the bases. The cross-section of the cones and the plane is
A) a circle.
B) an ellipse.
C) a parabola.
D) a hyperbola.

Answer 1

Answer:

  D) a hyperbola

Step-by-step explanation:

IMO, the image is not helpful, as it suggests the ends of the curve are nearly parallel to each other. In fact, the ends of the curve asymptotically approach straight lines parallel to the sides of the cone. That is, there are asymptotes that form an X shape. This is a characteristic of a hyperbola.

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A parabola is formed when the plane cuts the cone parallel to one side. That cut plane only intersects one nap of the cone. At a shallower angle yet, one gets an ellipse. Parallel to a base, one gets a circle.