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Question

Find the length of major axis, the eccentricity the latus rectum, the coordinate of the centre, the foci, the vertices and the equation of the directrices of following ellipse:
x216+y29=1.

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Solution

Given equation of ellipse is
x216+y29=1
On comparing the given equation with x2a2+y2b2=1, we get
a=4,b=3
Since, a>b ,therefore the major axis is along the x-axis while the minor axis is along the y-axis.
Length of major axis =2a=8
Length of minor axis =2b=6
Eccentricity e=1b2a2=16916==74
Coordinates of the foci are (7,0) and (7,0)
The coordinates of the vertices are (4,0) and (4,0)
Length of latus rectum = 2b2a=2×94=92

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