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.$16x^2+y^2=16$

Solution: Given equation is,
$16x^2+y^2=16$
We will convert this equation into standard form.
$\Rightarrow \frac{16}{16}{x}^2+\frac{1}{16}{y}^2=1$
$\Rightarrow \frac{x^2}{1}+\frac{y^2}{16}=1$
So, this is our standard equation of ellipse with,
$a=1,b=4$
$c=\sqrt{b^2-a^2}=\sqrt{16-1}=\sqrt{15}$
Here, as $b>a$, major-axis will be $Y-$axis.
Now, foci will be $\left(0,\pm c\right)=\left(0,\pm \sqrt{15}\right).$
Vertices will be $\left(0,\pm b\right)=\left(0,\pm 4\right).$
Length of major-axis $=2b=8$
Length of minor axis $=2a=2$
Eccentricity $=\frac{c}{b}=\frac{\sqrt{15}}{4}.$
Length of latus rectum $=2\frac{a^2}{b}=2\ast \frac{1}{4}=\frac{1}{2}.$