Question

The foci of an ellipse lie on y-axis and are symmetrically situated about origin. The distance between foci is 24 and eccentricity of the ellipse is $\frac{12}{13}$. The equation of the ellipse must be

• A. $\frac{x^{2}}{144}$+ $\frac{y^{2}}{169}$= 1
• B. $\frac{x^{2}}{25}$+ $\frac{y^{2}}{144}$= 1
• C. $\frac{x^{2}}{25}$+ $\frac{y^{2}}{169}$= 1
• D. None of these

Answer 1

Answer: (C)

$\frac{x^{2}}{25}$+ $\frac{y^{2}}{169}$= 1

Answer 2

Ž SS¢ = 2be = 24

2b × $\frac{12}{13}$= 24 Q e = $\frac{12}{13}$

Ž b = 13

Q a² = b² (1 – e²) = 169 $\left( 1 - \frac{144}{169} \right)$= 25 Ž $\frac{x^{2}}{25}$+ $\frac{y^{2}}{169}$= 1