Conic Section PPT Maths Class 11

 Page 1


CONIC  SECTIONS
?
 Introduction
?
 Sections of a cone
?
 Circle
?
 Parabola
?
 Ellipse
?
 Hyperbola
Page 2


CONIC  SECTIONS
?
 Introduction
?
 Sections of a cone
?
 Circle
?
 Parabola
?
 Ellipse
?
 Hyperbola
INTRODUCTION:
Circles, ellipses, parabolas and hyperbolas are known as Conic Sections 
because they can be obtained as intersections of a plane with a double 
napped right circular cone.
DOUBLE NAPPED RIGHT CIRCULAR CONE
Let l be a fixed vertical line & m be another 
line intersecting it at a fixed point V & 
inclined to it at an angle a .Suppose we 
rotate the line m around the line l in such a 
way that the angle a remains constant. Then 
the surface generated is a double napped 
right circular hollow cone herein after 
referred as double napped right circular 
cone.
l
m
a
Page 3


CONIC  SECTIONS
?
 Introduction
?
 Sections of a cone
?
 Circle
?
 Parabola
?
 Ellipse
?
 Hyperbola
INTRODUCTION:
Circles, ellipses, parabolas and hyperbolas are known as Conic Sections 
because they can be obtained as intersections of a plane with a double 
napped right circular cone.
DOUBLE NAPPED RIGHT CIRCULAR CONE
Let l be a fixed vertical line & m be another 
line intersecting it at a fixed point V & 
inclined to it at an angle a .Suppose we 
rotate the line m around the line l in such a 
way that the angle a remains constant. Then 
the surface generated is a double napped 
right circular hollow cone herein after 
referred as double napped right circular 
cone.
l
m
a
The point V is called 
Vertex; the line l is axis 
of cone. The rotating 
line m is called a 
generator of cone. The 
vertex separates the 
cone into two parts is 
called nappes.
V
m
l
?
 CONIC SECTION FROM A 
NAPPED RIGHT CIRCULAR 
CONE:
If we take intersection 
of a plane with a 
cone, section so 
obtained is called 
conic section.
Page 4


CONIC  SECTIONS
?
 Introduction
?
 Sections of a cone
?
 Circle
?
 Parabola
?
 Ellipse
?
 Hyperbola
INTRODUCTION:
Circles, ellipses, parabolas and hyperbolas are known as Conic Sections 
because they can be obtained as intersections of a plane with a double 
napped right circular cone.
DOUBLE NAPPED RIGHT CIRCULAR CONE
Let l be a fixed vertical line & m be another 
line intersecting it at a fixed point V & 
inclined to it at an angle a .Suppose we 
rotate the line m around the line l in such a 
way that the angle a remains constant. Then 
the surface generated is a double napped 
right circular hollow cone herein after 
referred as double napped right circular 
cone.
l
m
a
The point V is called 
Vertex; the line l is axis 
of cone. The rotating 
line m is called a 
generator of cone. The 
vertex separates the 
cone into two parts is 
called nappes.
V
m
l
?
 CONIC SECTION FROM A 
NAPPED RIGHT CIRCULAR 
CONE:
If we take intersection 
of a plane with a 
cone, section so 
obtained is called 
conic section.
When ß = 90°, the 
section is a circle.
When a < ß < 
90°, the section 
is a ellipse.
When ß = a, 
the section is a 
parabola.
When 0 = ß < a, 
the plane cuts 
through both 
nappes & curves 
of intersection is a 
hyperbola.
Page 5


CONIC  SECTIONS
?
 Introduction
?
 Sections of a cone
?
 Circle
?
 Parabola
?
 Ellipse
?
 Hyperbola
INTRODUCTION:
Circles, ellipses, parabolas and hyperbolas are known as Conic Sections 
because they can be obtained as intersections of a plane with a double 
napped right circular cone.
DOUBLE NAPPED RIGHT CIRCULAR CONE
Let l be a fixed vertical line & m be another 
line intersecting it at a fixed point V & 
inclined to it at an angle a .Suppose we 
rotate the line m around the line l in such a 
way that the angle a remains constant. Then 
the surface generated is a double napped 
right circular hollow cone herein after 
referred as double napped right circular 
cone.
l
m
a
The point V is called 
Vertex; the line l is axis 
of cone. The rotating 
line m is called a 
generator of cone. The 
vertex separates the 
cone into two parts is 
called nappes.
V
m
l
?
 CONIC SECTION FROM A 
NAPPED RIGHT CIRCULAR 
CONE:
If we take intersection 
of a plane with a 
cone, section so 
obtained is called 
conic section.
When ß = 90°, the 
section is a circle.
When a < ß < 
90°, the section 
is a ellipse.
When ß = a, 
the section is a 
parabola.
When 0 = ß < a, 
the plane cuts 
through both 
nappes & curves 
of intersection is a 
hyperbola.
When we throw a ball, the path 
covered by the ball is parabolic.
This bridge is parabolic in 
nature.