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Conic Sections Ellipse & Hyperbola Class 11 | Ch-10

Conic Sections | Ellipse & Hyperbola | Chapter-11 | Class XI

Conic Section, Ellipse and its complete explanation with diagrams, Hyperbola and its complete explanation with diagrams
ELLIPSE
An ellipse is the set of all points in a plane sum of whose distances from two fixed points in the plane is a constant. The two fixed points are called foci.
Eccentricity < 1




CENTRE OF THE ELLIPSE:-
 The mid point of the line segment joining the foci is called the centre of the ellipse.
MAJOR AXIS:-
A line segment passing through the foci of the ellipse is called the major axis.
MINOR AXIS:-
A line passing through the centre of the ellipse and is perpendicular to the major axis is called minor axis.
ECCENTRICITY:-
It is defined as the ratio of the half of the  distance between the foci to the length of the semi major axis. Mathematically:-  e = c / a
LATUS RECTUM:-

It is the line segment perpendicular to the major axis through any of  the foci and whose end points lie on the ellipse. Mathematically Length of latus rectum is =\frac{2b^{2}}{a}\]
STANDARD EQUATIONS OF THE ELLIPSE:-

When major axis is along the x-axis then equation of the ellipse is

When major axis is along the x-axis then equation of the ellipse is
Where  equation

PROPERTIES OF ELLIPSE

HYPERBOLA:-
It is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is fixed or constant.  Eccentricity > 1
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TRANSVERSE AXIS:- 
The line through the focuses is called transverse axis. Length of transverse axis is 2a.
CONJUGATE AXIS:- 
A line through the centre and perpendicular to the transverse axis is called conjugate axis. Length of conjugate axis is 2b
Distance between two focii is 2c, where
ECCENTRICITY:- 
The ratio e = c/a is called eccentricity
LENGTH OF LATUS RECTUM:- 
It is the line segment perpendicular to the transverse axis through any of the focuses and whose end points lie on the hyperbola.
STANDARD EQUATIONS OF HYPERBOLA:-
When major axis is x-axis then equation of hyperbola is 
equation 
When major axis is y-axis then equation of hyperbola is
 equation 
PROPERTIES OF HYPERBOLA

Art Integrated Project on Conic Section Class 11

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Maths Conic Section Part 2 Class 11 NCERT-cbse mathematics


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