1. The origin is the center of the hyperbola. Thus the general equation of the hyperbola is
2. You know at least 2 points of the hyperbola: (2,0), (4,2). The coordinates of these points must satisfy the equation of the hyperbola. Plug in the coordinates and solve the system of equations for a and b. I've got
The equation of the hyperbola is:
3. The points B and D are symmetric by reflection over the x-axis. You only need to know the y-coordinate of B to calculate the distance BD. The x-coordinate of B is 3. Plug in this value and solve the equation of the hyperbola for y:
The point B has the coordinates: ; point D is at
4. rounded to the nearest centimeter the distance is 3 cm.