Correct Answer - Option 3 :
\(\frac{\sqrt{5}}{3}\)
Formula used:
The eccentricity of the ellipse:
\(e\ =\ \sqrt{1-\frac{b^2}{a^2}}\)
Calculation:
Given that,
\(4x^2 + 9y^2 - 8x - 36y + 4 = 0\)
This can be written as
\((2x - 2)^2 + (3y - 6)^2 = 36\)
⇒ \(\frac{(x-1)^2}{9} + \frac{(y-2)^2}{4}=1\)
Hence eccentricity is
\(\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{4}{9}}\)
\(\Rightarrow\ e\ =\frac{\sqrt{5}}{3}\)
