This topic analyzes and examines the knowledge of conic curve, straight line and circle, and examines the ability of students to solve problems by using what they have learned.

(1) The equation of straight line can be obtained from the intersection of straight line (1, 3) and slope, and the midpoint of the intersection of straight line and hyperbola at BD is (1, 3). We can work out the relationship between A and B according to the formula of midpoint coordinates after removing straight lines and hyperbolas, that is, we can get eccentricity.

(2) Using eccentricity, the condition | fa ||| FB | = 1 7 is expressed as an algebraic expression containing a, and then the coordinates of point A (1,0) can be obtained. Since A is on the X axis, it can be proved as long as 2AM=BD is proved.