Question

$\frac{y^2}{9}-\frac{x^2}{27}=1$

Find the eccentricity of the ellipse.

Answer 1

$\frac{y^2}{9}-\frac{x^2}{27}=1$

$\uparrow$

Equation of an ellipse

$a^2=27,b^2=9$

$a=\sqrt{27}b=3.$

$a=3\sqrt{3}$

e, eccentricity

$=\sqrt{\frac{1-b^2}{a^2}}=\sqrt{\frac{a^2-b^2}{a^2}}$

$=\sqrt{\frac{27-9}{27}}=\sqrt{\frac{18}{27}}$