Formula Used
Line general form: Ax + By + C = 0
Slope intercept: y = mx + b → mx - y + b = 0
Point slope: y - y₁ = m(x - x₁) → mx - y + y₁ - mx₁ = 0
Two points: A = y₁ - y₂, B = x₂ - x₁, C = x₁y₂ - x₂y₁
Circle general form: x² + y² + Dx + Ey + F = 0
Quadratic conic form: Ax² + Bxy + Cy² + Dx + Ey + F = 0
How To Use This Calculator
- Select the equation style you want to convert.
- Enter the requested values in the visible fields.
- Choose decimal precision and normalization options.
- Press the convert button.
- Review the general form result above the form.
- Use the graph to confirm the shape visually.
- Download the CSV or PDF file when needed.
Example Data Table
| Input Type | Sample Input | General Form Output |
|---|---|---|
| Slope intercept | y = 2x + 3 | 2x - y + 3 = 0 |
| Two points | (1, 2), (6, 7) | x - y + 1 = 0 |
| Circle standard | (x - 2)² + (y + 3)² = 25 | x² + y² - 4x + 6y - 12 = 0 |
| Quadratic | y = x² - 4x + 3 | x² - 4x - y + 3 = 0 |
Convert Equations Into General Form
Why General Form Matters
A general form calculator changes common equation styles into a standard algebra layout. This layout makes comparison easier. It also makes graphing and checking simpler.
For a line, the common target is Ax + By + C = 0. The coefficients show slope, intercept behavior, and direction. The calculator can start from slope intercept form, point slope form, two points, intercept form, or a direct line form. It then expands, moves every term to one side, and simplifies the equation.
Circle And Conic Conversion
For a circle, the target is usually x² + y² + Dx + Ey + F = 0. The tool expands the standard circle form. It also supports circle diameter endpoints. This is useful when a geometry problem gives two opposite points instead of a center and radius.
For a quadratic relation, the result is written as Ax² + Bxy + Cy² + Dx + Ey + F = 0. This wider conic layout also fits parabolas. It keeps every coefficient visible. That helps when you need a clean conversion for reports or homework.
Cleaner Algebra Results
The calculator includes a precision option. It also includes a positive leading coefficient option. Decimal inputs can be scaled into an integer-like equation. This is helpful when an answer should look neat. The tool still shows the original conversion steps, so the method stays clear.
The graph adds a visual check. A line, circle, or parabola appears below the answer. This helps you notice mistakes in signs, points, or radius values. It also makes the result easier to explain.
Exports And Review
Use the CSV export when you need spreadsheet data. Use the PDF export when you need a quick report. Both exports collect the main equation, coefficients, and summary values.
This calculator is best for learning, reviewing, and checking algebra conversions. It is not a proof assistant. Always check special cases, such as zero intercepts, identical points, or missing terms. Those cases can change the meaning of the equation.
Teachers can use it for examples. Students can compare several forms quickly. Designers can save a repeatable conversion record. The layout keeps inputs, results, formulas, and downloads in one clear page, so each step remains easy to follow daily.
FAQs
What is general form?
General form places all equation terms on one side and sets the other side to zero. Lines usually use Ax + By + C = 0.
Can this calculator convert circle equations?
Yes. It converts center-radius form and diameter endpoint form into circle general form with x², y², x, y, and constant terms.
Can decimals be converted into integer coefficients?
Yes. Select the integer scaling option. The calculator multiplies coefficients by a power of ten and reduces common factors when possible.
Why is the leading coefficient made positive?
A positive leading coefficient gives a cleaner final equation. Multiplying every term by negative one does not change the equation meaning.
Does the graph prove the answer?
The graph is a visual check, not a formal proof. It helps confirm shape, slope, center, radius, and obvious sign errors.
What happens if two points are identical?
Identical points do not define a unique line. The calculator shows an error and asks for two different points.
Can I export the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.
Is this useful for homework?
Yes. It shows formulas, steps, coefficients, examples, and graph output. You can review each conversion before submitting your work.