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Śrīmad-Bhāgavatam 1.3.11

షష్ఠమత్రేరపత్యత్వం వృత: ప్రాప్తోఽనసూయయా । ఆన్వీక్షికీమలర్కాయ ప్రహ్లాదాదిభ్య ఊచివాన్ ॥ ౧౧ ॥
ṣaṣṭham atrer apatyatvaṁ
[shashtham atrer apatyatvam]
vṛtaḥ prāpto ’nasūyayā
[vritah praapto ’nasooyayaa]
ānvīkṣikīm alarkāya
[aanveekshikeem alarkaaya]
prahlādādibhya ūcivān
[prahlaadaadibhya oochivaan]
Word-for-word
ṣaṣṭham — the sixth one atreḥ — of Atri apatyatvam — sonship vṛtaḥ — being prayed for prāptaḥ — obtained anasūyayā — by Anasūyā ānvīkṣikīm — on the subject of transcendence alarkāya — unto Alarka prahlāda-ādibhyaḥ — unto Prahlāda and others ūcivān — spoke.
Blended reading (Sanskrit + English inline)
ṣaṣṭham atrer apatyatvaṁ
ṣaṣṭham
the sixth one
atreḥ
of Atri
apatyatvam
sonship
vṛtaḥ prāpto ’nasūyayā
vṛtaḥ
being prayed for
prāptaḥ
obtained
ānvīkṣikīm alarkāya
anasūyayā
by Anasūyā
prahlādādibhya ūcivān
ānvīkṣikīm
on the subject of transcendence
alarkāya
unto Alarka
prahlāda-ādibhyaḥ
unto Prahlāda and others
ūcivān
spoke.
The sixth incarnation of the puruṣa was the son of the sage Atri. He was born from the womb of Anasūyā, who prayed for an incarnation. He spoke on the subject of transcendence to Alarka, Prahlāda and others [Yadu, Haihaya, etc.].
Purport

The Lord incarnated Himself as Dattātreya, the son of Ṛṣi Atri and Anasūyā. The history of the birth of Dattātreya as an incarnation of the Lord is mentioned in the Brahmāṇḍa Purāṇa in connection with the story of the devoted wife. It is said there that Anasūyā, the wife of Ṛṣi Atri, prayed before the lords Brahmā, Viṣṇu and Śiva as follows: “My lords, if you are pleased with me, and if you desire me to ask from you some sort of blessings, then I pray that you combine together to become my son.” This was accepted by the lords, and as Dattātreya the Lord expounded the philosophy of the spirit soul and especially instructed Alarka, Prahlāda, Yadu, Haihaya, etc.

— A.C. Bhaktivedanta Swami Prabhupāda
Gauḍīya Ācāryas
Viśvanātha Cakravartī Ṭhākura Gauḍīya
Translation
Being requested by Anasūyā, the wife of Atri, the Lord became her son as Dattātreya and taught knowledge of the soul to Alarka, Prahlāda and others.
Commentary

Being selected by Anasūyā, the wife of Atri, he became her son. This is described in the Brahmāṇḍa Purāṇa in the story of the pativrata:

anasūyābravīn natvā devān brahmeśa-keśavān | yūyaṁ yadi prasannā me varārhā yadi vāpy aham | prasādābhimukho bhūtvā mama putratvam eṣyatha ||

Offering respects, Anasūyā spoke to the Brahmā, Śiva and Viṣṇu. If you are pleased with me, and consider me worthy of blessing, being merciful, you should become my son.

Ānvīkṣikīm means knowledge of the ātmā.

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