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

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.