18. The ellipse $E : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ ($a > b > 0$) passes through the point $(0, \sqrt { 2 })$, and has eccentricity [Figure] (1) Find the equation of ellipse $E$; (2) The line $x = m y - 1$ ($m \in \mathbb{R}$) intersects the ellipse $E$ at points $A$ and $B$. Determine the positional relationship between the point $G \left( - \frac { 9 } { 4 } , 0 \right)$ and the circle with diameter $AB$, and explain the reason.
(1) Find the equation of ellipse $E$; (1) Find the equation of ellipse $E$;
(2) The line $x = m y - 1$ ($m \in \mathbb{R}$) intersects the ellipse $E$ at points $A$ and $B$. Determine the positional relationship between the point $G \left( - \frac { 9 } { 4 } , 0 \right)$ and the circle with diameter $AB$, and explain the reason. [Figure]
18. The ellipse $E : \frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$ ($a > b > 0$) passes through the point $(0, \sqrt { 2 })$, and has eccentricity\\
\includegraphics[max width=\textwidth, alt={}, center]{af8058d3-52ab-42d0-ba33-0c5c3a276f48-03_378_410_904_1306}\\
(1) Find the equation of ellipse $E$;\\
(2) The line $x = m y - 1$ ($m \in \mathbb{R}$) intersects the ellipse $E$ at points $A$ and $B$. Determine the positional relationship between the point $G \left( - \frac { 9 } { 4 } , 0 \right)$ and the circle with diameter $AB$, and explain the reason.
\section*{(1) Find the equation of ellipse $E$; \\
(1) Find the equation of ellipse $E$;}
(2) The line $x = m y - 1$ ($m \in \mathbb{R}$) intersects the ellipse $E$ at points $A$ and $B$. Determine the positional relationship between the point $G \left( - \frac { 9 } { 4 } , 0 \right)$ and the circle with diameter $AB$, and explain the reason.\\
\includegraphics[max width=\textwidth, alt={}, center]{af8058d3-52ab-42d0-ba33-0c5c3a276f48-03_405_408_1265_1482}