Question

The eccentricity of the ellipse 5x² + 9y² = 1 is
(a) 2/3
(b) 3/4
(c) 4/5
(d) 1/2

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\frac{2}{3} \\ 5x^2+9y^2=1 \\ \Rightarrow \frac{x^2}{5}+\frac{y^2}{9}=1 \\ \therefore a=\sqrt{5}\mathrm{and}b=3 \\ \mathrm{Here},b>a,\mathrm{so}\mathrm{the}\mathrm{major}\mathrm{and}\mathrm{the}\mathrm{minor}\mathrm{ax}es\mathrm{of}\mathrm{the}\mathrm{ellipse}\mathrm{are}\mathrm{along}\mathrm{the}x-axis\mathrm{and}they-\mathrm{axis},\mathrm{respectively}. \\ \mathrm{Now},e=\sqrt{1-\frac{a^2}{b^2}} \\ \Rightarrow e=\sqrt{1-\frac{5}{9}} \\ \Rightarrow e=\sqrt{\frac{4}{9}} \\ \Rightarrow e=\frac{2}{3} \end{gathered}$$