Conic Sections Flashcards
(10 cards)
are the curves obtained from the intersection between a double-napped cone and a plane.
Conic sections
the non-degenerate conic sections,
parabola,
ellipse,
hyperbola,
circle
One type of ellipse
a circle,
Then the resulting surface is referred as double-napped right circular cone.
double-napped right circular
hollow cone
are formed when the plane is parallel to the generating line of one cone or if the angle between the
plane and the axis is equal to the vertex angle.
Parabola
formed when the plane is tilted such that angle between the plane and the axis is greater than the vertex
angle but less than 90°
Ellipse
are formed when the plane is parallel to the axis of revolution or the y-axis. If the angle formed
between the plane and the axis is less than the vertex angle but greater than or equal to zero.
Hyperbolas
are formed when the intersection of the plane is perpendicular to the axis of revolution.
Circles
are formed when a plane intersects the cone in such a way that it passes through the
vertex.
Degenerate conic sections
three degenerate conic sections
single point,
line,
and two
intersecting lines