Question

Find the co-ordinates of focii of the ellipse $\frac{x^2}{100}+\frac{y^2}{36}=1$.

Answer 1

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

Now the eccentricity of the ellipse is $\sqrt{1-\frac{36}{100}}=\sqrt{\frac{64}{100}}=\frac{8}{10}=\frac{4}{5}$.

Now the co-ordinates of the focii are $(\pm 5\times \frac{4}{5},0)=(\pm 4,0)$.