geo point

For MySQL 5.7+

Given we have the following simple table,

create table example (
  id bigint not null auto_increment primary key,
  lnglat point not null
);

create spatial index example_lnglat
    on example (lnglat);

With the following simple data,
insert into example (lnglat)
values
(point(-2.990435, 53.409246)),
(point(-2.990037, 53.409471)),
(point(-2.989736, 53.409676)),
(point(-2.989554, 53.409797)),
(point(-2.989350, 53.409906)),
(point(-2.989178, 53.410085)),
(point(-2.988739, 53.410309)),
(point(-2.985874, 53.412656)),
(point(-2.758019, 53.635928));

POINT(lng, lat)
You would get the points within a given range of another point (note: we have to search inside a polygon) with the following combination of st functions:

set @px = -2.990497;
set @py = 53.410943;
set @range = 150; -- meters
set @rangeKm = @range / 1000;

set @search_area = st_makeEnvelope (
  point((@px + @rangeKm / 111), (@py + @rangeKm / 111)),
  point((@px - @rangeKm / 111), (@py - @rangeKm / 111))
);

select id,
       st_x(lnglat) lng,
       st_y(lnglat) lat,
       st_distance_sphere(point(@px, @py), lnglat) as distance
  from example
 where st_contains(@search_area, lnglat);


You should see something like this as a result:

3   -2.989736   53.409676   149.64084252776277
4   -2.989554   53.409797   141.93232714661812
5   -2.98935    53.409906   138.11516275402533
6   -2.989178   53.410085   129.40289289527473

For reference on distance, if we remove the constraint the result for the test point looks like this:

1   -2.990435   53.409246   188.7421181457556
2   -2.990037   53.409471   166.49406509160158
3   -2.989736   53.409676   149.64084252776277
4   -2.989554   53.409797   141.93232714661812
5   -2.98935    53.409906   138.11516275402533
6   -2.989178   53.410085   129.40289289527473
7   -2.988739   53.410309   136.1875540498202
8   -2.985874   53.412656   360.78532732013963
9   -2.758019   53.635928   29360.27797292756

Note 1: the field is called lnglat since that's the correct order if you think of points as (x, y) and is also the order most functions (like point) accept the parameter

Note 2: you can't actually take advantage of spatial indexes if you were to use circles; also note that the point field can be set to accept null but spatial indexes can't index it if it's nullable (all fields in the index are required to be non-null).

Note 3: st_buffer is considered (by the documentation) to be bad for this use case

Note 4: the functions above (in particular st_distance_sphere) are documented as fast but not necessarily super accurate; if your data is super sensitive to that add a bit of wiggle room to the search and do some fine tuning to the result set
//https://stackoverflow.com/questions/2411528/query-points-within-a-given-radius-in-mysql

SELECT ST_Buffer( point(1.967817, 2.043222), 1)
SELECT
contains(
    ST_Buffer( point(1.967817, 2.043222), 1),
          point(1.967817, 2.043222)
         )
         SELECT
  contains(
     st_makeEnvelope (
  point((1.967817 + 100 / 111), (2.043222 + 100 / 111)),
  point((1.967817 - 100 / 111), (2.043222 - 100 / 111))
    )
      ,
          point(1.967817, 2.043222)
         )

https://dev.mysql.com/doc/refman/5.6/en/spatial-operator-functions.html
https://www.percona.com/blog/2013/10/21/using-the-new-mysql-spatial-functions-5-6-for-geo-enabled-applications/
https://mariadb.com/kb/en/library/st_centroid/