Question

Find the length of major axis, minor axis, latus rectum and eccentricity of the ellipse $9x^2+16y^2=144$

Answer 1

Given equation can be written in standard form as $\frac{x^2}{16}+\frac{y^2}{9}=1$

$\Rightarrow a^2=16,b^2=9\Rightarrow a=4,b=3$

So length of Major axis $=2a=8$

and length of Minor axis $=2b=6$

Also eccentricity$,e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}$

And length of latus rectum $=\frac{2b^2}{a}=\frac{2\cdot 9}{4}=\frac{9}{2}$