Given that we need to find the eccentricity of the ellipse 9x² + 25y² - 18x - 100y - 116 = 0.

⇒ 9x² + 25y² - 18x - 100y - 116 = 0

⇒ 9(x² - 2x + 1) + 25(y² - 4y + 4) - 225 = 0

⇒ 9(x - 1)² + 25(y - 2)² = 225

⇒

⇒

Comparing with the standard form

Here a²>b²

⇒ eccentricity(e) =

⇒

⇒

⇒

∴ The correct option is B