This is a presentation for class assessment

1. Mathematics is , In Mathematics
is , in its way , the Poetry of ,Logical
Ideas ! – ALBERT EINSTEIN
Mathematics
Presentation
on Conic sections
(Second Term)
Class : 11-C
Name : Poorva

2. INTRODUCTION :-
The concept of conic sections is really interesting to
study as it includes the scrutiny of various shapes
like circles , ellipses , parabolas and hyperbolas .
The names parabola and hyperbola are given by
Apollonius . These curves are known as conic
sections because they are obtained as intersections
of a plane with a double napped right circular
cone . These curves have a very wide range of
applications in fields such as planetary motion ,
design of telescopes , reflectors of flashlights etc .
Concept Conic Sections

3. Circles
A Circle is the set of all points in a
plane that are equidistant from a
fixed point in the plane .
The fixed point is called centre of the
circle and the distance from the
centre to a point on the circle is called
the radius of the circle .
Formula of a circle is :-

4. A parabola is the set of all points in a plane that
are equidistant from a fixed line and a fixed point
( not on the line ) in the plane .
The fixed line is called ‘ directrix of the line’ and
the fixed point is called the ‘ focus’ . A line
through the focus and perpendicular to the
directrix is called the ‘ axis of the parabola ‘ . The
point of intersection of parabola with the axis is
called the ‘ vertex ‘ of the parabola .
parabolas

5. The equation of a parabola is simplest if
the vertex is at the origin and the axis
of symmetry is along x-axis or y-axis .
The four possible orientations are :
1) y^2 = 4ax
2) y^2 = -4ax
3) x^2 = 4ay
4) x^2 = -4ay
LATUS RECTUM : - It is the line
perpendicular to the axis of parabola
through the focus and whose end
points lie on the parabola . It is given
by ,
Length of latus rectum = 4a
Standard equation

6. An ellipse is the set of all points in a
plane the sum of whose
distances from two fixed points in
the plane is constant .The two
fixed points are called foci . The
line segment through the foci of
ellipse is called major axis and
the line segment through the
centre and perpendicular to the
major axis is called the minor
axis. The end points of the major
axis are called the vertices of the
ellipse .
Ellipse
The constant which is the sum
of distances of a point on the
ellipse from the two fixed
points is always greater than
the distance between the two
fixed points .
Note :-

7. Relation between semi-major
axis, semi-minor axis and the
distance of focus :-
C^2 = a^2 – b^2
ECCENTRICITY :- The eccentricity
of an ellipse is the ratio of the
distances from the centre of the
ellipse to one of the foci and to
one of the vertices .
E = c/a and e<1

8. The equation of an ellipse is
simplest if the centre of the ellipse
is at origin and the foci are on the
x-axis and y-axis . The two
possible orientations are :
1)When x-axis is the major axis-
x^2/a^2 + y^2/b^2 = 1
2) When y-axis is the major axis-
x^2/b^2 + y^2/a^2 = 1
Standard equations :-
Latus rectum
is given by -
2b^2/a

9. Hyperbola – A hyperbola is the set of
all points in a plane the difference of
whose distances from fixed points is
constant .
The line through foci is called the transverse axis
and the line perpendicular to it is called conjugate
axis . The points at which both the axes intersect is
called vertices .

10. Eccentricity :-
The ratio of e=c/a is
called the eccentricity
of hyperbola . c > a , so
the eccentricity can
never be less than one .
Latus rectum :-
It is the line segment
perpendicular to the
transverse axis
through any foci and
whose end points lie
on hyperbola .