$20\%)$ Given the language L $=\{$wxwR: w$\{$a$,$ b$\}*,$ x is a fixed terminal symbol$\},$ answer the following questions:

$($a$)$ Write the context$-$free grammar that generates L

$($b$)$ Construct the pda that accepts L from the grammar of $($a$)$

$($c$)$ Construct the pda that accepts L directly based on the similar skill used in wwR$.$

$($d$)$ Is this language a deterministic context$-$free language?