get meta value using get_result

I want to get a json print with some of my posts in a specific category.

I want ex.: title, category and then some meta-data with the keyes lat and lon (coordinates).

Case:
[{"lat":"55.395263","lon":"10.385723","post_title":"Mammas Pizza","post_cat":"Fast Food")"}

Here is one of my tests:

$result = $wpdb->get_results("SELECT a.*, b.* FROM $wpdb->posts a LEFT JOIN $wpdb->postmeta b ON b.post_id = a.ID");

	if (!$result['error']) {
		print json_encode($result);
	} else {
		errorJson('fail');
	}

How can I get a json with these data using get_results?