When a right circular cone is cut by a plane which is parallel to

When a right circular cone is cut by a plane which is parallel to
| When a right circular cone is cut by a plane which is parallel to the slant line, the obtained conic section will be

A. Circle

B. Ellipse

C. Parabola

D. Hyperbola

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Right Answer is: C

SOLUTION

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:

  • 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). 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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