жмякай на кнопку и смотри во кладке network куда и какой запрос уходит
в твоем случае уходит POST запрос с параметром method=getImage
dka@desktop ~ % http -vv -f POST https://rand.by/ajax.php method=getImage
POST /ajax.php HTTP/1.1
Accept: */*
Accept-Encoding: gzip, deflate
Connection: keep-alive
Content-Length: 15
Content-Type: application/x-www-form-urlencoded; charset=utf-8
Host: rand.by
User-Agent: HTTPie/2.1.0
method=getImage
HTTP/1.1 200 OK
Connection: keep-alive
Content-Encoding: gzip
Content-Type: text/html; charset=UTF-8
Date: Tue, 12 May 2020 15:27:00 GMT
Server: nginx/1.10.3 (Ubuntu)
Transfer-Encoding: chunked
{
"image": "http://farm66.static.flickr.com/65535/49887294892_1fc5852dd3_b.jpg"
}