18. (This problem is worth 16 points) As shown in the figure, in the rectangular coordinate system xOy, given that the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ has eccentricity $\frac { \sqrt { 2 } } { 2 }$, and the distance from the right focus F to the left directrix l is 3. [Figure] (1) Find the standard equation of the ellipse; (2) A line through F intersects the ellipse at points $\mathrm { A } , \mathrm { B }$. The perpendicular bisector of segment AB intersects the line l and AB at points $\mathrm { P } , \mathrm { C }$ respectively. If $\mathrm { PC } = 2 \mathrm { AB }$, find the equation of line AB.
18. (This problem is worth 16 points)\\
As shown in the figure, in the rectangular coordinate system xOy, given that the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$ has eccentricity $\frac { \sqrt { 2 } } { 2 }$, and the distance from the right focus F to the left directrix l is 3.\\
\includegraphics[max width=\textwidth, alt={}, center]{02c41b96-8a48-49a2-8c05-38046d0bc54f-2_396_444_1932_230}\\
(1) Find the standard equation of the ellipse;\\
(2) A line through F intersects the ellipse at points $\mathrm { A } , \mathrm { B }$. The perpendicular bisector of segment AB intersects the line l and AB at points $\mathrm { P } , \mathrm { C }$ respectively. If $\mathrm { PC } = 2 \mathrm { AB }$, find the equation of line AB.\\