### Example 5 of how to find the equation of a hyperbola

In xy-plane, M(x, y) is a moving point. F_{2}(13, 0) is a fixed point. L is a fixed line with the equation x = 144/13. The distance from the moving point M to the fixed line L is d.
The distance from the moving point M to the fixed point F_{2} is MF. The ratio of MF to d is the constant 13/12. What is the equation for the moving point M?