Question

Find the equation of the directrix of the ellipse $\frac{x^2}{100}+\frac{y^2}{36}=1$.

Answer 1

Given the equation of the ellipse $\frac{x^2}{100}+\frac{y^2}{36}=1$.

Now comparing this equation with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ we get, $a=10,b=6$.

Then eccentricity $\left(e\right)=\sqrt{1-\frac{b^2}{a^2}}$$=\sqrt{1-\frac{36}{100}}=\sqrt{\frac{64}{100}}=\frac{8}{10}.$

Now equations of directrix are

$x=\pm \frac{a}{e}=\pm \frac{10}{\frac{8}{10}}$ or, $8x=\pm 100$ or, $2x=\pm 25$.