Question: If the eccentricity of the ellipse $\frac{x^{2}}{a^{2} + 2} + \frac{y^{2}}{a^{2} + 5}$= 1 be\(\fra...

Question

If the eccentricity of the ellipse $\frac{x^{2}}{a^{2} + 2} + \frac{y^{2}}{a^{2} + 5}$ = 1 be $\frac{1}{\sqrt{3}}$ , then length of latus rectum of ellipse is

Answer 1

Solution

Clearly a² + 5 > a² + 2

So (a² + 2) = (a² + 5) $\left( 1 - \frac{1}{3} \right)$

3a² + 6 = 2a² + 10 Ž a² = 4

\ equation of ellipse is $\frac{x^{2}}{6} + \frac{y^{2}}{9} = 1$

\ length of latus rectum = $\frac{2 \times 6}{3} = 4$

Question: If the eccentricity of the ellipse \(\frac{x^{2}}{a^{2} + 2} + \frac{y^{2}}{a^{2} + 5}\)= 1 be\(\fra...

Solution