Dynamic dropdown editing in laravel

I have a dynamic catagory dropdown. i want to update the dynamic dropdown?

public function update(Request $request, $id)

  {
        $this ->validate($request,[
            'name' => 'required',
            'catagory' => 'required'
]}
        $catagory= Catagory::find($id);
$catagory = DB::table('catagories as a')
            ->join('catagories as b', 'a.P_id', '=', 'b.id')
            ->select('a.name','a.P_id')
            ->get();
        $catagory->name=$request->name;
        $catagory->P_id=$request->P_id;
        $catagory->SaveCategory();

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