Answer:
y = - [tex]\frac{1}{32}[/tex] x²
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-0)^2+(y+8)^2}[/tex] = | 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 = - [tex]\frac{1}{32}[/tex]x²
