Question

In each of the Exercises $1$ to $9$, 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.
$\frac{x^2}{16}+\frac{y^2}{9}=1$

Answer 1

$\frac{x^2}{16}+\frac{y^2}{9}=1---(10$

$a=4b=3$

$h=0k=0$

$\Rightarrow$ Centre of given ellipse $=(h,k)=(0,0)$

$\to$ length of major axis $=2a=8$

$\to$ length of minor axis $=25=6$

$\to$ eccentricity$\left(e\right)=\sqrt{\frac{a^2-b^2}{a^2}}=\frac{\sqrt{7}}{4}$

$\to$ Vertices $=(4,0)$ & $(-4,0)$

$\to$ co-vertices $=(0,3)$ & $(0,-3)$

$\to$ focii $=(\sqrt{7},0)$ & $(-\sqrt{7},0)$

$\to$ length of latus rectum $=\frac{2b^2}{c^2}=\frac{2\times 9}{4}=\frac{9}{2}$