The given equation is 16x2+y2=16
It can be written as
16x2+y2=16
x21+y216=1
x212+y242=1...(1)
Herethe denominator of y242 is greater than the denominator of x212
Therefore, the major axis is along the y-axis while the minor axis is along the x-axis.
On comparing equation (1) with x2b2+y2a2=1, we obtain b=1 and a=4
∴ae=c=√a2−b2=√16−1=√15
Therefore, the coordinates of the foci are (0,±√15)
The coordinates of the vertices are (0,±4)
Length of major axis =2a=8
Length of minor axis =2b=2
Eccentricity e= ca=√154
Length of latus rectum = 2b2a=2×14=12