What is the equation of a parabola with focus (0,-8) and directrix y=8?

y = - x²

Step-by-step explanation:

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

Using the distance formula

= | y - 8 |

Square both sides

x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides

x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )

x² + 32y = 0 ( subtract x² from both sides )

32y = - x² ( divide both sides by 32 )

y = - x²