WordPress multiple Ajax Search URLs

I'm using typeahead to enhance the search on my woocommerce website. Therefore I'd like to split products and content results for different FE-Display.

Im using the wp-admin/admin-ajax.php?action=ajax_search&fn=get_ajax_search&terms=[searchterm] to receive the results. Im trying to add something like "&posttype=post" or "&posttype=product" or "&posttype=page" to get different results.

But it seems, as it has no effect on the results. I can't limit the searchresults posttypes on the input field as I need all of these 3 resulttypes (and maybe more). Is there any chance to get different ajax-search URLs limited to the posttype?

Thank you in advance

thanks to @Bijal Patel I found the solution:

I've added a new action "shop_search" and made up several different search queries which can be called using &pts=posttype so I can go for different searches like ?action=shop_search&pts=product&terms=test in functions

add_action( 'wp_ajax_nopriv_shop_search', 'shop_search' );
add_action( 'wp_ajax_shop_search', 'shop_search' );

and then just like

function shop_search() {
if ( isset( $_REQUEST['pts'] ) && 'product' == $_REQUEST['pts'] ) { //pts = post type search // looking for Posttype = product
    $product_query = new WP_Query( array(
        's' => $_REQUEST['terms'],
        'post_type' => 'product', // Posttype goes here
        //'posts_per_page' => 10,
        'no_found_rows' => true,
    ) );

    $presults = array( );

    if ( $product_query->get_posts() ) {

        foreach ( $product_query->get_posts() as $the_post ) {

            Do STUFF 

            $presults[] = array(
                'lorem' => $ipsum,
                'foo' => $bar,
            );
        }

    } else {
        $presults[] = __( 'Sorry. No results match your search.', 'wp-typeahead' );
    }

    wp_reset_postdata();
    echo json_encode( $presults );
}

can be endless like...

if ( isset( $_REQUEST['pts'] ) && 'post' == $_REQUEST['pts'] ) { //pts = post type search // Posttype = post
    $product_query = new WP_Query( array(
        's' => $_REQUEST['terms'],
        'post_type' => 'post', // posttype goes here
        //'posts_per_page' => 10,
        'no_found_rows' => true,
    ) );

   $results = array( );
// see above for what to do next
// And Close it all afterwards
    die(); }

For all the posttypes I have to query, this may not be the fastest solution. If you just have to seperate between 2 or 3 posttypes, this will be it, more or less. Call the searchresults using: mysite.com/wp-admin/admin-ajax.php?action=shop_search&pts=product&terms=test

So if anyone has an idea how to speed things up, please tell me! Thank you. And a special Thank you to Bijal - you made my weekend!