### Example 1 of a hyperbola

In xy-plane, M(x, y) is a moving point. F_{1}(-5, 0) and F_{2}(5, 0) are two fixed points. If the absolute value of the distance MF1 subtract the distance MF2 is 8, then what is the locus of the moving point M?

In a plane, if the absolute value of the difference between the distance from a moving point to a fixed point and the distance from the moving point to another fixed point is a constant that is
less than the distance between two fixed points, then the locus of the moving point is a hyperbola.

Draw a line that pass through these two fixed points as x-axis. Draw a line that pass through the midpoint of these two fixed points and perpendicular to the line that has these two fixed points as the y-axis.