In diagram 1 the length "a"  that is in black is the distance from the Vertex point P to the focus point F.  If a line segment is constructed that is perpendicular to the axis of symmetry and passes through the focus point F of a parabola connecting both sides of the parabola, this line will always have a length of (4a).  This line segment is called the Latus Rectum which is in blue in diagram 1. 

This also means that the focus point F is the midpoint of the latus rectum.  So the distance from an endpoint of the latus rectum to the focus point F is always (2a), where "a" is the distance from the vertex to the focus point.   Therefore, if we know the coordinates of the focus point F and the distance "a" from the vertex to the focus point, we can determine the coordinates of the endpoints of the latus rectum.

In diagram 2 below, the focus point F is at ( 2, 7 ) and the distance "a" is equal to 3.  In this situation, the two endpoints of the latus rectum will be at

                 ( x - 2a, y )   and   ( x + 2a, y )

where ( x, y ) represents the focus point.  Since the focus point is at ( 2, 7 ), then the endpoints of the latus rectum are at

                 ( 2 - (2 · 3), 7 )   and   ( 2 + (2 · 3), 7 )

                 ( 2 - 6, 7 )           and   ( 2 + 6, 7 )

                 ( -4, 7 )               and   ( 8, 7 )

In diagram 3 below, the distance to the two endpoints of the latus rectum from the focus point F is equal to the distance from the directrix to the two endpoints of the latus rectum according to the geometric definition of a parabola.  So the distance from the two endpoints of the latus rectum to the directrix is also "2a".  This is easy to see in this situation because the distance from the vertex point P to the directrix is also equal to "a".