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Example 1 of a hyperbola

In xy-plane, M(x, y) is a moving point. F1(-5, 0) and F2(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.