Basics & Formulas Ch-10 Class11 | Conic Sections Ellipse & Hyperbola
Conic Sections | Ellipse & Hyperbola | Chapter-11 | Class XI
Conic Section, Ellipse and its complete explanation with diagrams, Hyperbola and its complete explanation with diagrams
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.
The mid point of the line segment joining the foci is called the centre of the ellipse.
MINOR AXIS:-
A line passing through the centre of the ellipse and is perpendicular to the major axis is called 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
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 =
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 =
STANDARD EQUATIONS OF THE ELLIPSE:-
When major axis is along the y-axis then equation of the ellipse is
Where 
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
TRANSVERSE AXIS:-
The line through the focuses is called transverse axis. Length of transverse axis is 2a.
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
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
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.
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
When major axis is y-axis then equation of hyperbola is
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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