When the cutting plane is inclined to the axis of the cone the curve of intersection obtained is an?

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When the cutting plane is inclined to the axis of the cone the curve of intersection obtained is an?

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Cone: A cone is obtained by revolving a right-angled triangle about its perpendicular side which remains fixed.

When a right circular cone is cut by planes at different angles to its axis, depending on the angle of the cutting plan, four different curves are formed. These curves are called conic sections.

The different conic sections are:

When the cutting plane is inclined to the axis of the cone the curve of intersection obtained is an?

  • Circle: cutting plane is parallel to the base of the cone (or perpendicular to the axis of the cone)
  • Parabola: a cutting plane is parallel to the lateral side/slant line (or generator) 
  • Ellipse: cutting plane is oblique to the cone (not parallel nor perpendicular to any element) and it cuts all its generator
  • The cutting plane is making a greater angle with the axis, more than half of the included angle of the cone.
  • Hyperbola: a cutting plane is parallel to the axis of the cone not passing through the vertex

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