Śrīmad-Bhāgavatam 10.50.9
Blended reading (Sanskrit + English inline)
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avatāraḥ
—
descent
Ava + √tṛ — 'crossing down.' In Gauḍīya tattva, an avatāra is not God 'becoming' something less; it is the original Bhagavān crossing down into a particular līlā-medium. Kṛṣṇa's appearance here is svayam-bhagavān-avatāra, the source of all others.
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bhū-bhāra-haraṇāya
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for removing the burden of the earth
Triple compound: bhū + bhāra + haraṇa. The signature mission-statement of Kṛṣṇa's manifest pastime. The 'burden' is not weight but the adharmic kings whose presence the earth itself cannot tolerate (cf. SB 1.17 — earth as cow).
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saṁrakṣaṇāya
—
for the complete protection
Sam + rakṣaṇa — total, not partial, protection. Of sādhus specifically: the sādhu is the one whose only refuge is Kṛṣṇa, and protecting him is the Lord's vow (Gītā 9.31, kaunteya pratijānīhi).
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vadhāya
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for killing
Vadha-, the formal act of executing the duṣkṛtas. Kṛṣṇa's vadha is itself a benediction — the asura killed by His hand attains liberation. Demonology in Gauḍīya frame is never merely punitive; it is also salvific.
"I have come as Krsna avatara with this purpose: for relieving the burden of the earth (destroying the armies), for protecting the devotees; and for killing the demons."
The purpose is this (etad-arthaḥ). I have appeared on earth to relieve the burden of the earth. Śrīdhara Svāmī accepts the version with ayam since he refers to it later in his commentary. Sometimes the word hi (certainly) is seen instead. The second line makes clear what was stated in the first line. I descend to protect the devotees and kill the non-devotees. The word saṁ--rakṣanāya is used to indicate protect in this life and the next, since the devotees spread bhakti.
The avatāra descends from Vaikuṇṭha. “Will be devotees also be killed in relieving the earth of her burden?” No, the devotees will be protected. Only the non-devotees will be killed. The word saṁ--rakṣanāya is used to indicate protection in this life and the next, since the devotees spread bhakti. Or “The person killed by you, though not qualified, will get liberation.” The purpose of the avatāra is to give liberation to those who are a burden to the earth. The method is given: to protect the devotees and kill the wicked, later giving them liberation. In this avatāra which reveals unlimited powers, the devotees will be protected and the wicked will be killed.
The Lord names His own purpose in a single breath, as a goldsmith calls the metal by its alloy: avatāra to lift the burden, protect the sādhus, kill the asuras. The verse is a near-prose echo of Gītā 4.7-8 spoken now in action rather than in instruction.
On the chariot at Kurukṣetra Kṛṣṇa told Arjuna yadā yadā hi dharmasya glāniḥ — whenever dharma declines, I descend to protect the sādhus, destroy the duṣkṛtas, and re-establish dharma. SB 10.50.9 is the field-deployment of that same proposition: a few generations earlier, outside besieged Mathurā, He names the same threefold purpose.
Gauḍīya ācāryas read this as evidence that the avatāra-prayojana doctrine is not theoretical — it is the load-bearing skeleton of every līlā, including the killing of Jarāsandha's twenty-three armies.
My note
Source: vedabase.io