URL url =  new  URL("http://localhost:8080/?q1s=triangle&q1xr=0.5&q1yr=0.5&x=1&y=1&R=2");

HttpURLConnection httpURLConnection = (HttpURLConnection) url.openConnection();
httpURLConnection.setRequestMethod("GET");
httpURLConnection.connect();

serverSocket =  new  ServerSocket( 8080 );
...
Socket socket = serverSocket.accept();
...
// Достаем параметры
BufferedReader reader =  new  BufferedReader( new  InputStreamReader(inputStream));
String readedLine = reader.readLine();

...
       Simple-Request = "GET" SP Request-URI CRLF

       Full-Request   = Request-Line             ; Section 5.1
                        *( General-Header        ; Section 4.3
                         | Request-Header        ; Section 5.2
                         | Entity-Header )       ; Section 7.1
                        CRLF
                        [ Entity-Body ]          ; Section 7.2
...
       Request-Line = Method SP Request-URI SP HTTP-Version CRLF

URL url =  new  URL("http://localhost:8080");

URLConnection urlConnection = url.openConnection();
urlConnection.setDoOutput(true);

OutputStream outputStream = urlConnection.getOutputStream();
outputStream.write("GET /?q1s=triangle&q1xr=0.5&q1yr=0.5&x=1&y=1&R=2 HTTP/1.0 \r\n".getBytes());

outputStream.flush();
outputStream.close();

httpURLConnection.connect();

 int  responseCode = httpURLConnection.getResponseCode();
 if  (responseCode != HttpURLConnection.HTTP_OK) {
    ... // Дальнейшие действия
}