ABC is a right-angled scalene triangle

In this case we have the hyperbola again. While it seems obvious that the locus will pass through B the vertex at the right angle (obvious since this will be the Orthocenter (H)) The question to be asked is can we predict through wich of the remaining vertices will the hyperbola pass and which one will it merely touch?

Claim: The hyperbola passes through the vertex at which the triangle has the smallest angles while touching at the vertex at which the middle sized angle.

To test the claim and watch a GSP sketch draw the locus click here.