Q. 84.2( 15 Votes )

In each of the, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.

16x2 + y2 = 16

Answer :

The given equation is 16x2 + y2 = 16.


It can be written as


16x2 + y2 = 16


Or, =1


Or, =1. ………… (1)


Here, the denominator of is greater than the denominator of.


Therefore, the major axis is along the x-axis, while the minor axis is along the y-axis.


On comparing the given equation with =1, we obtain b =1 and a =4.


c = =


Therefore,


The coordinates of the foci are ().


The coordinate of the vertices are (0, ).


Length of major axis = 2a = 8


Length of minor axis = 2b = 2


Eccentricity, e


Length of latus rectum =


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