A researcher selects two points on the same hyperbola and measures their distances to the two foci. For the first point, the distances are $13$ and $5$. For the second point, the distances are $20$ and $12$. What is the best conclusion?

The data are consistent only if the two points are vertices

The data are inconsistent because one point must be closer to both foci

The data are consistent with the hyperbola’s focal property because both absolute differences equal $8$

The data are inconsistent because the sums of the distances are not equal