### Dictionary Rank of a Word | Permutations & Combinations

PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

### Conic Sections / Ellipse & Hyperbola / Chapter-11 / Class XI

Maths Conic Section Part 2 Class 11 NCERT-cbse mathematics

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.

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:-

$When\; major\; axis\; is\; along \; the\; x-axis\; then\; equation \; of \; the\; ellipse\; is\; \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$
$When\; major\; axis\; is\; along \; the\; y-axis\; then\; equation \; of \; the\; ellipse\; is\; \frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1$$c^{2}=a^{2}-b^{2}$

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.

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
$Distance\; between\; two\; focuses \; is = 2c ,where\; \; c^{2}=a^{2}+b^{2}$
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.

Maths Conic Section Part 2 Class 11 NCERT-cbse mathematics
STANDARD EQUATIONS OF HYPERBOLA:-
$When\; major\; axis \: \: is\: x-axis\: then \: equation\: of\: hyperbola\: is \: \: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$$When\; major\; axis \: \: is\: y-axis\: then \: equation\: of\: hyperbola\: is \: \: \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1$

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