Ajax request is empty when it gets to controller laravel

Question

Ajax request is empty when it gets to controller laravel. How to solve this.

Inside form tag i have a search field.

<div class="form-row ">
    <div class="col-sm-6 col-md-2 col-lg-2 mb-4">
        <div class="select-wrap">
            <input type="text" name="name" id="name" class="form-control" placeholder="Search By Name">
        </div>
    </div>
    <div class="col-sm-6 col-md-2 col-lg-2 mb-4"> 
        <button id="search" class="btn btn-primary">Search</button>
    </div> <!-- end of serach warap  -->
</div>

Ajax

function search() {
    var form_data = {
        search_name:$('#name').val(),
        org_type:$('#type_of_organization').val(),
        city:$('#city_id').val(),
        type:$('#type').val(),
        start_price:$('#amount_start').val(),
        end_price:$('#amount_end').val(),
        check_in:$('#check_in').val(),
        check_out:$('#check_out').val(),
    } //end of var

    if(form_data) {
        $.ajax( {
            type:"GET",
            url:"{{route('local.search')}}?search="+form_data,
            dataType:'json',
            data:form_data,
            success:function(res){
                console.log(res);
            }
        }
    }
}

function registorEvents(){
    $(document).on('click','#search',search);
}

registorEvents();

The problem is, it is rendering a blank page and changing my url from ../book/create to ../book

APIController

public function localSearch(Request $request) { 
    if($request->ajax()) {
        $name=$request->get('name');
        $org_type=$request->get('org_type');
    }
 .....
}

Route

Route::get('api/local-search','APIController@localSearch')->name('local.search');