If the distance from a point P on hyperbola x2-y23 = 1 to the left focus is 4, then the distance from point P to the right collimator is () A. 1b. 2C. 3D. 1 or 3

If the distance from a point P on hyperbola x2-y23 = 1 to the left focus is 4, then the distance from point P to the right collimator is () A. 1b. 2C. 3D. 1 or 3

In hyperbola x2-y23 = 1, a = 1, B = 3, C = 2, e = 2. The distance from point P to its right focus is ± 2 + 4 = 6 or 2. Let the distance from point P to its right collimator be X. from the second definition of hyperbola, we can see that 6X = 2 or 2x = 2, and the solution is x = 3 or 1. Therefore, the distance from point P to its right collimator is 3 or 1