JEE Main 2024 Mathematics question

The differential equation of the family of circles passing the origin and having center at the line y = x is:

• (A)(x² − y² + 2xy)dx = (x² − y² + 2xy)dy
• (B)(x² + y² + 2xy)dx = (x² + y² − 2xy)dy
• (C)(x² − y² + 2xy)dx = (x² − y² − 2xy)dyCorrect
• (D)(x² + y² − 2xy)dx = (x² + y² + 2xy)dy