Q. 94.3( 3 Votes )

Find the (i) leng

Answer :


Given:


3x2 + 2y2 = 18


Divide by 18 to both the sides, we get



…(i)



Since, 6 < 9


So, above equation is of the form,


…(ii)


Comparing eq. (i) and (ii), we get


a2 = 9 and b2 = 6


a = √9 and b = √6


a = 3 and b = √6


(i) To find: Length of major axes


Clearly, a < b, therefore the major axes of the ellipse is along y axes.


Length of major axes = 2a


= 2 × 3


= 6 units


(ii) To find: Coordinates of the Vertices


Clearly, a > b


Coordinate of vertices = (0, a) and (0, -a)


= (0, 6) and (0, -6)


(iii) To find: Coordinates of the foci


We know that,


Coordinates of foci = (0, ±c) where c2 = a2 – b2


So, firstly we find the value of c


c2 = a2 – b2


= 9 – 6


c2 = 3


c = √3 …(I)


Coordinates of foci = (0, ±√3)


(iv) To find: Eccentricity


We know that,



[from (I)]


(v) To find: Length of the Latus Rectum


We know that,





= 4


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