The eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0 is

Given that we need to find the eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0.

⇒ 4x² + 9y² + 8x + 36y + 4 = 0

⇒ 4(x² + 2x + 1) + 9(y² + 4y + 4) - 36 = 0

⇒ 4(x + 1)² + 9(y + 2)² = 36

⇒

⇒

Comparing with the standard form

Here a²>b²

⇒ eccentricity(e) =

⇒

⇒

⇒

∴ The correct option is D