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.