If an agreement for the support of the petitioner is brought about, it must be reduced to writing and submitted to the family court or a support magistrate appointed pursuant to section four hundred thirty-nine of this act for approval. If the court or support magistrate approves it, the court without further hearing may thereupon enter an order for the support of the petitioner by the respondent in accordance with the agreement, which shall be binding upon the respondent and shall in all respects be a valid order as though made after process had been issued out of the court. The court record shall show that such order was made upon agreement.
N.Y. Family Court Law § 425