A case-inflected word denoting a quadruped is compounded with the co-ordinate word garbhiṇī and the resulting compound is tat-puruṣa ,
गोगर्भिणी 'a pregnant cow.' अजागर्भिणी 'a pregnant she-goat.'
Vart:- It should be stated that the rule is confined to the words denoting genus of quadrupeds. So not here:- कालाक्षी गर्भिणी or स्वस्तिमती गर्भिणी 'the pregnant cow called Kálákshí or Svastimatí'.
Why do we say 'quadrupeds ?' Observe ब्राह्मणी गर्भिणी.,