A plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone. What conic section is formed?

Question

Darren Atkinson

Mathematics

13 August, 18:40

A plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone. What conic section is formed?

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Answers (1)

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Jaylee · Answer 1

When a plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone, the conic section that is formed by the intersection is a curve known as hyperbola.

The standard form of the equation of the hyperbola is shown below:

[ (x-h) ^2/a^2]-[ (y-k) ^2/b^2]=1 (Horizontal axis)

[ (y-k) ^2/a^2]-[ (x-h) ^2/b^2]=1 (Vertical axis)

Therefore, the answer is: Hyperbola.