Double Math

What is Conic Sections

Conic sections or simply conics are the curves obtained by cutting a (double) right circular cone by a plane. Let RS be a line through the center C of a given circle and perpendicular to its plane. Let A be a fixed point on RS. All lines through A and points on the circle generate a right circular cone.

what is Conic Sections

Conic Sections

  • Nappes:Two parts of cone are called nappes.
  • vertex or apex: meeting point of two parts of cone are called apex or vertex.
  • circle: if cone is cut by the plane perpendicular the axes of the cone then resulting section is called circle. we an also define circle as “A locus of points which remains at a fixed distance from a certain point.” the point is called the Centre of circle and fixed distance is called the radius of circle.
  • Parabola of conic sections: If the intersecting plane is parallel to the generator of the cone but cut only one nappe is called parabola.
  • Ellipse of conic sections: If the cone is cut by the plane and the cutting plan is slightly titled and cut only one nappes of the cone then the resulting section is ellipse.
  • Hyperbola of conic sections: If the cone is cut by the plane and the cutting plan is parallels to the axis of the cone and intersects both its nappes , then curve of intersection is hyperbola.
  • Point circle: If a plane passes through the vertex of the cone, the intersection is a single point or point circle if r=0
  • Tangent: A line that touch the curve without cutting through it is called tangent.
  • Normal: A line perpendicular to the tangent is called normal
  • Chord of contact: A line joining point of contact of chord.
  • Eccentriity :The number e is called eccentricity where e=\frac{\left|PF\right|}{\left|PM\right|}
  • Centeral conic: ellipse and hyperbola are called central conics.