document.write( "Question 737426: if a right circular cone intersects a plane that goes through both nappes of the cone, but not through the vertex, the resulting curve will be an \n" ); document.write( "

Algebra.Com's Answer #450373 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "If the angle of the plane is $\"less\"$ than the angle of the cone, then the intersection is a $\"point\"$ . \r
\n" ); document.write( "\n" ); document.write( "If the angle of the plane is $\"greater\"$ than the angle of the cone, then the intersection is $\"two\"$ $\"+lines\"$ intersecting at the vertex.\r
\n" ); document.write( "\n" ); document.write( "If the plane insersects at $\"other\"$ than the $\"vertex\"$ , then the intersection is a $\"circle\"$ when the plane is $\"perpendicular\"$ to the cone's axis, an $\"ellipse\"$ when the plane's angle is $\"less\"$ than the cone's angle, a $\"parabola\"$ when the planes's angle $\"equals\"$ the cone's angle, and two $\"hyperbola\"$ 's in the last case.\r
\n" ); document.write( "\n" ); document.write( "If a right circular cone is intersected by a plane so that the intersection goes $\"through\"$ the cone's $\"vertex\"$ as well as an $\"edge\"$ of each nappe, the shape produced is a $\"line\"$ .\r
\n" ); document.write( "\n" ); document.write( "in your case, if a right circular cone intersects a plane that goes through both nappes of the cone, but not through the vertex, the resulting curve will be a $\"hyperbola\"$ \r
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