Search for Hospitals and Clinics near a particular zip code - google-maps-api-3

Question

I would like to know a method to search for hospitals or clinics within a particular radius around a pin code. How do I go about this and integrate it into my website? I would be using google maps api for the first time so please try and use simple terms.
Okay so I manage to do this much
<script type="text/javascript">
var map;
var infowindow;
var geocoder;
var lat;
var lng;
var custom;
function initialize() {
geocoder = new google.maps.Geocoder();
var address = "Mumbai 400004";
geocoder.geocode({ 'address': address}, function(results, status) {
if (status == google.maps.GeocoderStatus.OK) {
lat = results[0].geometry.location.lat();
lng = results[0].geometry.location.lng();
custom = new google.maps.LatLng(lat, lng);
map.setCenter(custom);
}
});
var mapOptions = {
zoom: 12,
center: custom,
mapTypeId: google.maps.MapTypeId.ROADMAP
}
map = new google.maps.Map(document.getElementById("map_canvas"), mapOptions);
var request = {
location: custom,
radius: 500,
types: ['hospital']
};
infowindow = new google.maps.InfoWindow();
var service = new google.maps.places.PlacesService(map);
service.nearbySearch(request, callback);
}
function callback(results, status) {
if (status == google.maps.places.PlacesServiceStatus.OK) {
for (var i = 0; i < results.length; i++) {
createMarker(results[i]);
}
}
}
function createMarker(place) {
var placeLoc = place.geometry.location;
var marker = new google.maps.Marker({
map: map,
position: place.geometry.location
});
google.maps.event.addListener(marker, 'click', function() {
infowindow.setContent(place.name);
infowindow.open(map, this);
});
}
</script>
the problem now is that markers for hospitals are not showing on the map. What mistake have I made here ? Thank you for your help.