Find records by given latitude and longitude which intersects and circle within 2 mile radius using PostGIS?

I have a Postgres table with some data created by using a shapefile. I need to find all records which intersect within 2 miles radius from a given latitude and longitude. I used some queries including the following one.

SELECT * FROM us_census_zcta WHERE ST_INTERSECTS(geom, CIRCLE(POINT(40.730610, -73.935242), 2));

But none of them worked. What I am doing wrong here? How can I get the results I need?

The SRID is 4269 (NAD 83).

EDIT: After Mike Organek pointed me out that I have switched the lat-long in the above query. And then I tried a few things and the following query gave me 1 record.

SELECT * FROM us_census_zcta WHERE ST_INTERSECTS(geom::geometry, ST_SETSRID(ST_POINT(-73.935242, 40.730610), 4269)::geometry);

But how can I use Circle and find records which intersect within 2 miles radius from that given lat-long?

Solution

What you're looking for is ST_DWithin, which will check if records intersect within a given buffer. In order to use it with miles you better cast the geometry column to geography, as it then computes distances in metres:

For geography: units are in meters and distance measurement defaults to use_spheroid=true. For faster evaluation use use_spheroid=false to measure on the sphere.

SELECT * FROM us_census_zcta 
WHERE 
  ST_DWithin(
    geom::geography, 
    ST_SetSRID(ST_MakePoint(-73.935242, 40.730610), 4269)::geography,
    3218.688); -- ~2 miles

Keep in mind that this cast might affect query performance if the indexes aren't set properly.