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