In the causative a new agent appears, and the old one (the प्रयोज्य) has to go
somewhere. 1.4.52 makes it a कर्म — द्वितीया — when the root means motion,
perceiving/knowing, eating, has speech as its object, or has no object. Otherwise it
stays a कर्ता, and, unexpressed, goes to तृतीया. Kātyāyana's vārttikas on the sūtra,
as the corpus has them:
Two matter here: दृशेश्च adds दृश् (seeing is not
“knowing”, so it needed adding) and अदिखाद्योर्न removes अद्
and खाद् — so with the same English verb “eat”, भुज् gives
but खाद् gives .
In the causative passive, the Mahābhāṣya on 1.4.51 says
ण्यन्ते कर्तुश्च कर्मणः — the प्रयोज्य, now a कर्म, is what the
passive expresses: . Where the प्रयोज्य stayed
a कर्ता, the passive expresses the ordinary object instead:
.