Q. 15.0( 5 Votes )

Find the (i) leng

Answer :


Given:


…(i)



Since, 25 > 9


So, above equation is of the form,


…(ii)


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


a2 = 25 and b2 = 9


a = √25 and b = √9


a = 5 and b = 3


(i) To find: Length of major axes


Clearly, a > b, therefore the major axes of the ellipse is along x axes.


Length of major axes = 2a


= 2 × 5


= 10 units


(ii) To find: Coordinates of the Vertices


Clearly, a > b


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


= (5, 0) and (-5, 0)


(iii) To find: Coordinates of the foci


We know that,


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


So, firstly we find the value of c


c2 = a2 – b2


= 25 – 9


c2 = 16


c = √16


c = 4 …(I)


Coordinates of foci = (±4, 0)


(iv) To find: Eccentricity


We know that,



[from (I)]


(v) To find: Length of the Latus Rectum


We know that,





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