I.) Here are some important formulae of ELLIPSE which can help a lot in this topic while doing Prepare For JEE/AIEEE ..

                    WHEN EQUATION OF ELLIPSE IS 

1.) Coordinates of the centre = (0,0)

2.) Coordinates of the vertices = (a,0) and (-a,0)

3.) Coordinates of foci = (ae,0) and (-ae,0)

4.) Length of the major axis = 2a

5.) Length of the minor axis =2b

6.) Equation of the major axis = y=0

7.) Equation of the minor axis = x =0

8.) Equations of the directrices = x = a/e and x = - a/e

9.) Eccentricity = e = ( 1- b^2/a^2)^1/2 

10.) Length of the latus rectum = 2b^2/a

11.) Focal distances of a point (x,y) = a+-ex ( a plus minus ex)

II.)

                          WHEN THE EQUATION OF THE ELLIPSE IS 

1.) Coordinates of the centre = (0,0)

2.) Coordinates of the vertices = (0,b) and (0,-b)

3.) Coordinates of the foci = (0,be) and (0,-be)

4.) Length of the major axis = 2b

5.) Length of the minor axis = 2a

6.) Equation of the major axis = x =0

7.) Equation of the minor axis = y=0

8.) Equations of the directrices = y = b/e and y = -b/e

9.) Eccentricity = e = (1- a^2/b^2)^1/2

10.) Length of the latus-rectum = 2a^2/b

11.) Focal distances of the point (x,y) = b+-ey ( b plus minus ey)

12.) I hope this will help a lot to the readers and they'll find this topic quite easier..

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