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y = (x + 2)²

Step-by-step explanation:

Any point on the parabola (x, y) is equidistant from the focus and directrix.

Using the distance formula

= | y + 3 |

Square both sides

(x + 2)² + (y - 3)² = (y + 3)² ← expand the factors in y

(x + 2)² + y² - 6y + 9 = y² + 6y + 9 ← subtract y² + 6y + 9 from both sides

(x + 2)² - 12y = 0 ← subtract (x + 2)² from both sides

- 12y = - (x + 2)² ( divide both sides by - 12 )

y = (x + 2)²