Flashcards: Hyperbola | Mathematics (Maths) for JEE Main & Advanced PDF Download

 Page 1


 
 
 
CONIC SECTIONS 
Conic sections, namely a point, pair of straight lines, circle, ellipse, parabola and hyperbola are called so 
because they can be obtained when a cone (or double cone) is cut by a plane. 
The mathematicians associated with the study of conics were Euclid, Aristarchus and Apollonius. Most 
of the objects around us and in space have shape of conic-sections. Hence study of these becomes a very 
important tool for present knowledge and further exploration. 
  
Page 2


 
 
 
CONIC SECTIONS 
Conic sections, namely a point, pair of straight lines, circle, ellipse, parabola and hyperbola are called so 
because they can be obtained when a cone (or double cone) is cut by a plane. 
The mathematicians associated with the study of conics were Euclid, Aristarchus and Apollonius. Most 
of the objects around us and in space have shape of conic-sections. Hence study of these becomes a very 
important tool for present knowledge and further exploration. 
  
 
 
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(i) When a double right circular cone is cut by a plane parallel to base at the common vertex, the cutting 
profile is a point. 
  
Page 3


 
 
 
CONIC SECTIONS 
Conic sections, namely a point, pair of straight lines, circle, ellipse, parabola and hyperbola are called so 
because they can be obtained when a cone (or double cone) is cut by a plane. 
The mathematicians associated with the study of conics were Euclid, Aristarchus and Apollonius. Most 
of the objects around us and in space have shape of conic-sections. Hence study of these becomes a very 
important tool for present knowledge and further exploration. 
  
 
 
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(i) When a double right circular cone is cut by a plane parallel to base at the common vertex, the cutting 
profile is a point. 
  
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(ii) When a double right circular cone is cut by plane, parallel to its common axis, the cut profile is 
hyperbola 
 
  
Page 4


 
 
 
CONIC SECTIONS 
Conic sections, namely a point, pair of straight lines, circle, ellipse, parabola and hyperbola are called so 
because they can be obtained when a cone (or double cone) is cut by a plane. 
The mathematicians associated with the study of conics were Euclid, Aristarchus and Apollonius. Most 
of the objects around us and in space have shape of conic-sections. Hence study of these becomes a very 
important tool for present knowledge and further exploration. 
  
 
 
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(i) When a double right circular cone is cut by a plane parallel to base at the common vertex, the cutting 
profile is a point. 
  
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(ii) When a double right circular cone is cut by plane, parallel to its common axis, the cut profile is 
hyperbola 
 
  
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(iii) When a right circular cone is cut by a plane parallel to its base the cutting profile is a circle. 
 
  
Page 5


 
 
 
CONIC SECTIONS 
Conic sections, namely a point, pair of straight lines, circle, ellipse, parabola and hyperbola are called so 
because they can be obtained when a cone (or double cone) is cut by a plane. 
The mathematicians associated with the study of conics were Euclid, Aristarchus and Apollonius. Most 
of the objects around us and in space have shape of conic-sections. Hence study of these becomes a very 
important tool for present knowledge and further exploration. 
  
 
 
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(i) When a double right circular cone is cut by a plane parallel to base at the common vertex, the cutting 
profile is a point. 
  
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(ii) When a double right circular cone is cut by plane, parallel to its common axis, the cut profile is 
hyperbola 
 
  
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(iii) When a right circular cone is cut by a plane parallel to its base the cutting profile is a circle. 
 
  
 
 
 
Conic-sections as Sections of Right Circular 
Cone(s) 
(iv) When a right circular cone is cut by any plane through its vertex, the cutting profile is a pair of 
straight lines through its vertex