If F1 and F2 are the two focal points of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1, if the distance between a point m on the hyperbola and one of its focal points is equal to 16, find the distance between the other focal point
Hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1
Focus F1 (- 5,0), F2 (5,0)
If | MF1 | = 16,
When m is on the left branch,
|MF2|-|MF1|=2a=6
∴|MF2|=16+6=22
When m is on the right branch,
|MF1|-|MF2|=6
∴|MF2|=|MF1|-6=10
That is, the distance from m to another focus is 22 or 10