Calculator Inputs
Formula Used
Vertical parabola: (x − h)² = 4a(y − k)
Directrix: y = k − a
Focus: (h, k + a)
Horizontal parabola: (y − k)² = 4a(x − h)
Directrix: x = h − a
Focus: (h + a, k)
The calculator identifies the axis, extracts the focal distance a, then shifts one equal distance opposite the focus to locate the directrix.
How to Use This Calculator
- Select an input method that matches your problem statement.
- Enter the vertex parameters, vertex and focus, or expanded coefficients.
- Choose the correct orientation or equation type.
- Press Calculate Directrix to show the result above the form.
- Review the vertex form, axis, focus, opening direction, and solution steps.
- Use the CSV or PDF buttons to save the computed output.
Example Data Table
| Case | Input | Orientation | Vertex | a | Directrix |
|---|---|---|---|---|---|
| 1 | (x − 2)² = 12(y + 1) | Vertical | (2, -1) | 3 | y = -4 |
| 2 | (y + 4)² = -8(x − 5) | Horizontal | (5, -4) | -2 | x = 7 |
| 3 | Vertex (1, 3), Focus (1, 8) | Vertical | (1, 3) | 5 | y = -2 |
| 4 | x² - 8x - 4y + 20 = 0 | Vertical | (4, 1) | 1 | y = 0 |
FAQs
1. What is the directrix of a parabola?
The directrix is a fixed line used to define a parabola. Every point on the curve stays equally distant from the focus and the directrix.
2. How do I know whether the directrix is x = constant or y = constant?
If the parabola opens up or down, the directrix is horizontal, so it has y = constant. If it opens left or right, the directrix is vertical, so it has x = constant.
3. What does the value a mean here?
The value a is the signed distance from the vertex to the focus along the axis. The directrix lies the same distance from the vertex on the opposite side.
4. Can this calculator handle negative a values?
Yes. A negative a means the parabola opens downward or leftward, depending on orientation. The directrix automatically shifts to the opposite side of the vertex.
5. Why does the expanded equation need a selected type?
Expanded equations can describe vertical or horizontal parabolas. Choosing the correct form tells the calculator which variable to complete the square with first.
6. Can I use the focus and vertex option for tilted parabolas?
No. That option assumes a standard axis-aligned parabola. The vertex and focus must share the same x-coordinate or the same y-coordinate.
7. What output details are included besides the directrix?
The tool also shows the vertex, focus, axis of symmetry, opening direction, converted vertex form, and brief step-by-step working for verification.
8. When should I download CSV or PDF results?
Use CSV for spreadsheet storage and repeated comparisons. Use PDF when you want a clean worksheet record, classroom handout, or printable solution summary.