NGINX configuration for static and PHP files

I am trying to configure nginx to serve static and PHP files. The config I have isn't working. I want the following local folder structure:

src/static/  -> contains HTML, CSS, JS, images etc
src/api/     -> contains PHP files for a small REST service

If I visit http://mysite.local I want to be served files from the /static folder. If I visit http://mysite.local/api I want to be served the API PHP files. I want the requests to the api to be re-written and sent to an index.php file.

Some examples:

http://mysite.local/test.html                   -> served from src/static/test.html
http://mysite.local/images/something.png        -> served from src/static/images/something.png
http://mysite.local/css/style.css               -> served from src/static/css/style.css

http://mysite.local/api/users                   -> served from src/api/index.php?users
http://mysite.local/api/users/bob               -> served from src/api/index.php?users/bob
http://mysite.local/api/biscuits/chocolate/10   -> served from src/api/index.php?biscuits/chocolate/10

The below config works for static files but not for the api files. I get a 404 error back if I visit one of the API paths.

server {
    listen       80;
    server_name  mysite.local;
    access_log   /var/log/nginx/mysite.access.log main;
    error_log    /var/log/nginx/mysite.error.log debug;


    location / {
        index index.html;
        root /var/www/mysite/src/static;
        try_files $uri $uri/ =404;
    }

    location /api {
        index index.php;
        root /var/www/mysite/src/api;
        try_files $uri $uri/ /index.php?$query_string;

        location ~ \.php$ {
            try_files      $uri = 404;
            fastcgi_pass   127.0.0.1:9000;
            fastcgi_index  index.php;
            fastcgi_param  SCRIPT_FILENAME $document_root$fastcgi_script_name;
            include        fastcgi_params;
        }
    }
}