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Question

Find the coordinatesof the foce, 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
 



    Solution

    The correct option is

     the equation fo given ellipse is 
    16x2+y2=16
     i.e.  16x216+y216=1x21+y216=1Now16>1a2=16andb2=1So teh equation of ellipse in standard form is y2a2+x2b2=1a2=16a=4andb2=11We know that c=a2b2c=161=15Coordinates of foci(0,±c)i.e.(0,±15)Coordinates fo vertices are(0,±a)i.e.(0,±4)Length of major axis=2a=2×4=8Legnth of minor axis=2b=2×1=2Eccentricity(e)=ca=154Length of latus rectum=2b2a=2×14=12
     

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