Answer
$\frac{\sqrt 15}{4}$
Work Step by Step
First, we write our original equation in standard form:
Standard form in general is: $\frac{(x - h) ^{2}}{b^{2}}$ $+$ $\frac{(y - k) ^{2}}{a^{2}}$ $= 1$
$16$$x^{2}$ + $y^{2} = 16$ (original)
$\frac{x^{2}}{1}$ + $\frac{y^{2}}{16} = 16$ (standard form)
Graphing the equation, we find that the major axis is parallel to the y-axis.
This means $h = 0$; $k = 0$; $a = 4$; $b = 0$
The center of the ellipse is: $(h, k) = (0, 0)$
The vertices of the ellipse are:
$(h, k+a)$ and $(h, k-a)$ = $(0, 4)$ and $(0, -4)$
$c^{2} = a^{2} - b^{2} = 15$
The foci of the ellipse are:
$(h, k+c)$ and $(h, k-c)$ = $(0, \sqrt 15)$ and $(0, -\sqrt 15)$
Eccentricity $e = \frac{c}{a} = \frac{\sqrt 15}{4}$
