Testing geo bounds http://janmatuschek.de/LatitudeLongitudeBoundingCoordinates and http://gis.stackexchange.com/questions/19221/find-tangent-point-on-circle-furthest-east-or-west ; Detailed diagram for the same here http://gis.stackexchange.com/a/195148/61719

bounding_box_simple.py

from __future__ import division
import numpy as np

RADIUS_OF_EARTH_IN_KM = 6371.01 


def haversine(lat1, lon1, lat2, lon2):
  """
      Utility  to calcutlate distance between two pointtodo explain regarding height 
      coverting from geodisc co-ordinate to cartestian gives  errors when distances are further apart
  """
 
  dLat = np.radians(lat2 - lat1)
  dLon = np.radians(lon2 - lon1)
  lat1 = np.radians(lat1)
  lat2 = np.radians(lat2)
 
  a = np.sin(dLat/2)**2 + np.cos(lat1)*np.cos(lat2)*np.sin(dLon/2)**2
  c = 2*np.arcsin(np.sqrt(a))
 
  return RADIUS_OF_EARTH_IN_KM * c

from __future__ import division
import numpy as np

def get_bounding_box(distance, latittude, longitude):
    """
    Given a Geographic co-ordintate in degress, aim is to get a bounding box of a given point,
    basically a maximum latitude, minmun latitude and max longitude and min longitude based on explanation
    and formulae by these two sites
    http://janmatuschek.de/LatitudeLongitudeBoundingCoordinates
    http://gis.stackexchange.com/questions/19221/find-tangent-point-on-circle-furthest-east-or-west

    :param distance: bounding box distance in kilometer
    :param latittude: of the point of the center of the box
    :param longitude: of the point of the center of the box
    :return: top left co-ordinates, and top-right co-ordinates of the bounding box
    """
    # Convert to radians
    latittude = np.radians(latittude)
    longitude = np.radians(longitude)

    if not MIN_LATITUDE <= latittude <= MAX_LATITUDE:
        raise ValueError("Invalid latitude passed in")

    if not MIN_LONGITUDE <= longitude <= MAX_LONGITUDE:
        raise ValueError("Invalid longitude passed in")

    distance_from_point_km = distance
    angular_distance = distance_from_point_km / RADIUS_OF_EARTH_IN_KM

    # Moving along a latitude north or south, keeping the longitude fixed, is travelling along
    # a great circle; which means basically that doing so,the Radius from center of the earth ,
    # to the circle traced by such a path is constant; So to derive the top latitude and bottom latitude
    # without any error you just need to add or suntract the angular distance
    lat_min = latittude - angular_distance
    lat_max = latittude + angular_distance

    # Handle poles here
    if lat_min < MIN_LATITUDE or lat_max > MAX_LATITUDE:
        lat_min = max(lat_min, MIN_LATITUDE)
        lat_max = min(lat_max, MAX_LATITUDE)
        lon_max = MAX_LONGITUDE
        lon_min = MIN_LONGITUDE
        lat_max = np.degrees(lat_max)
        lat_min = np.degrees(lat_min)
        lon_max = np.degrees(lon_max)
        lon_min = np.degrees(lon_min)
        return (lat_min, lon_min), (lat_max, lon_max), lat_max

    # the latitude which intersects T1 and T2 in [1] and [2] is based on speherical trignomerty
    # this is just calculated for verifying this method
    latitude_of_intersection = np.arcsin(np.sin(latittude) / np.cos(angular_distance))
    latitude_of_intersection = np.degrees(latitude_of_intersection)

    # if we draw a circle  with distance around the lat and longitude, then the point where the
    # logitude touches the circle will be at a latitude a bit apart from the original latitiude as the
    # circle is on the sphere , the earths sphere
    delta_longitude = np.arcsin(np.sin(angular_distance) / np.cos(latittude))

    lon_min = longitude - delta_longitude
    lon_max = longitude + delta_longitude
    lon_min = np.degrees(lon_min)
    lat_max = np.degrees(lat_max)
    lon_max = np.degrees(lon_max)
    lat_min = np.degrees(lat_min)
    return (lat_min, lon_min), (lat_max, lon_max), latitude_of_intersection

Bounding Box
lat,long,angular_distance 13.08955 78.0335055556 0.000784584484057
delta_longitude 0.000805513923644 0.0461525481638
lat_min,lat_max 13.0445966204 13.1345033796
lon_min,lon_max 77.9873530074 78.0796581038
Distance from Point to T1 4.99859559377
Distnace from Point to T2 4.99859559377
Total time = 0.00556182861328

Poles are not handled currently

poles also handled

Looks like you forgot to convert lat_min to degrees.

good catch; will change; However the (latitude_of_intersection, min_longitude) is what defines the top left corner of the bounding box

   latitude1, longitude1 = 13.04738626, 77.61946793
    bounding_dist_in_meter = .500
    min_bound, max_bound, latitude_of_intersection = get_bounding_box(bounding_dist_in_meter, latitude1,
                                                                               longitude1)
    min_latitude, min_longitude = min_bound
    max_latitude, max_longitude = max_bound
    print min_latitude
    dist_to_t1 = haversine(latitude_of_intersection, min_longitude, latitude1, longitude1)
    dist_to_t2 = haversine(latitude_of_intersection, max_longitude, latitude1, longitude1)
    self.assertAlmostEqual(bounding_dist_in_meter, dist_to_t1, places=2)
    self.assertAlmostEqual(bounding_dist_in_meter, dist_to_t2, places=2)

Nice! Appreciate you sharing this. Thought you might want to know latitude is misspelled in the get_bounding_box function in several places stemming from the typo in the parameters for the function. Cheers