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Question

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 x249+y236=1.

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Solution

The given equation is x249+y236=1 or x272+y262=1
Her the donominator of x249is greater than the donominator of y236
Therefore the major axis is along the x-axis while the minor axis is along the y-axis
On comparing the given equation with x2a2+y2b2=1 we obtain a=7 and b=6
ae=c=a2b2=4936=13
Therefore, the coordinates of the foci are (±13,0)
The coordinates of the vertices are (±7,0)
Length of major axis =2a=14
Length of minor axis =2b=12
Eccentricity e= ca= 137
Length of latus rectum = 2b2a=2×367=727

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