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Example 5 of how to find the ellipse equation

In a xy-plane, M(x, y) is a moving point. F2(12, 0) is a fixed point. L is a line that has the equation x = 169/12. The distance from point M to L is d. The ratio of the distances MF2 to d is a constant which is 12 : 13. What is the equation for the point M(x, y)?

When a point M(x, y) moving in a xy-plane, if the distance between the moving point and a fixed point divide by the distance between the moving point and a fixed line is a constant and the constant is less than one, then the locus of the moving point is an ellipse. This is the second definition of an ellipse.