Parabola (Focus-Directrix Definition) Math Example 3

Solution

1. 1
   Step 1: Rewrite in standard form $x^2 = 4py$. From $y = \frac{1}{8}x^2$, multiply both sides by 8: $x^2 = 8y$.
2. 2
   Step 2: Compare with $x^2 = 4py$: $4p = 8$, so $p = 2$.
3. 3
   Step 3: Since $p > 0$ and the parabola opens upward, the focus is at $(0, p) = (0, 2)$.
4. 4
   Step 4: The directrix is the horizontal line $y = -p = -2$.