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Parabola Definition and Equation Calculator

Online parabola calculator: enter the parameter p to get the equation, focus (p/2,0) and directrix x=−p/2 (opens right).

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y²=2px, focus (p/2,0), directrix x=−p/2
Fl
Focus-to-directrix distance

📖 Tutorial | Parabola

1. Definition
Points equidistant from a focus F and a directrix l form a parabola; y²=2px has focus (p/2,0), directrix x=−p/2.
2. Formula & Notation
pFocus-to-directrix distance
3. Properties & Laws
  • Focus (p/2,0);
  • Directrix x=−p/2;
  • Eccentricity e=1;
  • Vertex is p/2 from each.
4. Steps
  1. Enter p>0;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: p=4: y²=8x, focus (2,0), directrix x=−2.
6. Common Pitfalls
Focus is p/2, not p;
Negative directrix;
One focus, one directrix.

❓ FAQ | Parabola

Definition?
Equal distances.
Focus?
(p/2,0).
Directrix?
x=−p/2.
e?
1.
Opens up?
x²=2py.
p?
Distance.
Vertex?
Origin.