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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.
36x2+4y2=144
 


Solution

The equation of given ellipse is, 
36x2+4y2=144
i.e.36x214+4y2144=1x24+y236=1.Now 36>4a2=36 and b2=4So the equation of ellipse in standard form isy2a2+x2b2=1
a2=36a=6 and b2=4b=2We know that c=a2b2c=364=32=42Coordinates of foci are (0,+c)i.e.(0,±2)Coordinates of vertices are (0,±a)i.e.(0,±6)Length of major axis=2a=2×6=12Length of minor axis=2b=2×2=4Eccentricity(e)=ca=426=223Length of latus rectum=2b2a=2×46=43
 


Mathematics

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