The eccentricity of the ellipse `4x^2+9y^2+8x+36 y+4=0` is a.`5/6` b. `3/5` c. `(sqrt(2))/3` d. `(sqrt(5))/3`

Explanation

`4 x^{2}+9 y^{2}+8 x+36 y+4=0`

`Rightarrow 4(x^{2}+2 x)+9(y^{2}+4 y)=-4`

`Rightarrow 4(x^{2}+2 x+1)+9(y^{2}+4 y+4)=-4+4+36`

`Rightarrow 4(x+1)^{2}+9(y+2)^{2}=36`

`Rightarrow frac{4(x+1)^{2}}{36}+frac{9(y+2)^{2}}{36}=1`

`Rightarrow frac{(x+1)^{2}}{9}+frac{(y+2)^{2}}{4}=1` Comparing it with `frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1`

a `=3` and `b=2`

`a=3` and `b=2`

...