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=1⇒x21+y216=1Now16>1⇒a2=16andb2=1So teh equation of ellipse in standard form is y2a2+x2b2=1∴a2=16⇒a=4andb2=1⇒1We know that c=√a2−b2∴c=√16−1=√15∴Coordinates 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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