Let the major axis is 2a.
Focus is (3,0) lies on x-axis.
Hence, Major axis of ellipse lies on x-axis.
Given that \(\frac{2b^2}{a}=\frac{2a}{2} ⇒\frac{2b^2}{a}=a\)
⇒ \(\)2b2 = a2 ⇒ \(b^2=\frac{a^2}{2}\) ----(i)
∴ \(e =\sqrt{1-\frac{b^2}{a^2}}\) \(= \sqrt{1 - \frac{1}{2}}\) (From (i))
= \(e =\frac{1}{√2}\)
∴ Focus of ellipse is (ae,o) = (3,0)
⇒ ae = 3
⇒ \(a×\frac{1}{√2}=3\)
⇒ \(a=3√2\)
∴ b2 = \(\frac{18}{2}\) = 9 (from (ii))
b = 3
Hence , equation of ellipse is
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
⇒ \(\frac{x^2}{18}+\frac{y^2}{9}=1\)
is equation of required ellipse.