1. Definition
Four forms: y²=2px right, x²=2py up, y²=−2px left, x²=−2py down; focus and directrix are symmetric about the vertex.
2. Formula & Notation
| p | Focus-to-directrix distance |
3. Properties & Laws
- Focus p/2 from vertex;
- Directrix on the other side;
- e=1;
- Vertex at origin.
4. Steps
- Pick a direction, enter p;
- Click "Find";
- Or click "Load Example".
5. Worked Examples
Example: right p=4: focus (2,0), directrix x=−2.
6. Common Pitfalls
Signs vary by direction;
p/2;
Opposite sides.