Question

The eccentricity of the ellipse 9x² + 25y² - 18x - 100y - 116 = 0 is

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{4}{5}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

$\frac{4}{5}$

Answer 2

If px² + qy² + 2rx + 25y +t = 0 represents on ellipse, then a² = qλ, b² = pλ

∴ e = $\sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\mspace{6mu} = \mspace{6mu}\sqrt{\frac{q - p}{q}} = \mspace{6mu}\sqrt{\frac{25 - 9}{25}} = \frac{4}{5}$