Question

If the foci of an ellipse are $( \pm \sqrt{5},0)$ and its eccentricity is $\frac{\sqrt{5}}{3}$, then the equation of the ellipse is

• A. 9x² + 4y² = 36
• B. 4x² + 9y² = 36
• C. 36x² + 9y² = 4
• D. 9x² + 36y² = 4

Answer 1

Answer: (B)

4x² + 9y² = 36

Answer 2

foci (± ae, 0) = (±$\sqrt{5}$, 0)

ae = $\sqrt{5}$ and e = $\frac{\sqrt{5}}{3}$ \ a = 3

Now b² = a²(1 – e²) ̃ b² = 9(1 – 5/9) = 4

\ eqⁿ $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ ̃ 4x² + 9y² = 36