Respuesta :

Answer:

y = [tex]\frac{1}{8}[/tex] x²

Step-by-step explanation:

For any point (x, y) on the parabola the focus and directrix are equidistant.

Using the distance formula

[tex]\sqrt{(x-0)^2+(y-2)^2}[/tex] = | y + 2 |

Square both sides

(x - 0)² + (y - 2)² = (y + 2)² ← expand parenthesis

x² + y² - 4y + 4 = y² + 4y + 4 ( subtract y² + 4y + 4 from both sides )

x² - 8y = 0 ( subtract x² from both sides )

- 8y = - x² ( divide both sides by - 8 )

y = [tex]\frac{1}{8}[/tex] x²