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
