Answer:
[tex]y=\frac{1}{4p}x^{2}[/tex]
Step-by-step explanation:
∵ The directrix is y = -p
∵ The focus is (0 , p)
∵ (x , y) is a general point on the parabola
∵ The distance between (x , y) and the directrix = the distance
between (x , y) and the focus
By using the rule of distance:
∵ (y - -p)² = (x - 0)² + (y - p)²
∴ (y + p)² = x² + (y - p)²
∴ y² + 2py + p² = x² + y² - 2py + p²
∴ 2py + 2py = x²
∴ 4py = x² ⇒ ÷ 4p in both sides
∴ [tex]y=\frac{1}{4p}x^{2}[/tex]
