Convert to General Form Calculator

Calculator

Conversion type

Decimal precision

Choose a model, enter values, and submit.

Line: y = mx + b

Slope m

Intercept b

Target form

Line: y - y1 = m(x - x1)

Slope m

Point x1

Point y1

Line through two points

Circle: (x - h)² + (y - k)² = r²

Center h

Center k

Radius r

Ellipse: (x - h)²/a² + (y - k)²/b² = 1

Center h

Center k

Semi-axis a

Semi-axis b

Vertical parabola: y = a(x - h)² + k

Horizontal parabola: x = a(y - k)² + h

Quadratic: y = ax² + bx + c

Reset

Example Data Table

Type	Input	General Form
Line	y = 2x + 3	2x - y + 3 = 0
Circle	(x - 2)² + (y + 3)² = 25	x² + y² - 4x + 6y - 12 = 0
Vertical parabola	y = 1(x - 2)² + 3	x² - 4x - y + 7 = 0
Ellipse	(x - 1)²/16 + (y + 2)²/9 = 1	9x² + 16y² - 18x + 64y - 71 = 0

Formula Used

Line y = mx + b becomes mx - y + b = 0.
Point slope y - y1 = m(x - x1) becomes mx - y + y1 - mx1 = 0.
Two points A = y1 - y2, B = x2 - x1, C = x1y2 - x2y1.
Circle (x - h)² + (y - k)² = r² becomes x² + y² - 2hx - 2ky + h² + k² - r² = 0.
Ellipse Multiply by a²b², expand, and collect all terms on the left.
Parabola Expand the vertex square, then move x or y terms to the left.

How to Use This Calculator

Select the equation type from the conversion menu.
Enter each known value in the related input fields.
Set decimal precision for the displayed answer.
Press the calculate button.
Read the result above the form.
Check coefficients and steps.
Download a CSV or PDF report when needed.

What Is General Form?

General form places every term on one side. The other side stays zero. This layout makes equations easier to compare. It also helps students identify coefficients quickly. A line often becomes Ax + By + C = 0. A conic often becomes Ax² + Bxy + Cy² + Dx + Ey + F = 0.

Why This Calculator Helps

Manual expansion can be slow. Small sign errors also happen often. This calculator expands common formats and returns a clear general form. It supports slope intercept lines, point slope lines, two point lines, circles, ellipses, parabolas, and quadratic models. Each option uses dedicated inputs. This keeps the process simple.

Using General Form In Class

Teachers use general form to compare equation families. Students use it before solving systems. It is also helpful for graphing. Coefficients show direction, shape, center terms, and constant shifts. Once the equation is expanded, many algebra steps become easier.

Accuracy And Workflow

Enter values carefully. Use negative signs when needed. Select the right equation type first. Then press the calculate button. The result appears above the form. Review the steps before exporting. You can download a CSV file for spreadsheets. You can also create a simple PDF report for notes.

Practical Examples

A circle in standard form can be expanded into general conic form. A line through two points can become one clean equation. A parabola in vertex form can be rewritten for comparison. These conversions are useful in homework, tutoring, design, and engineering checks.

Best Practices

Round only when your assignment allows rounding. Keep more decimal places for scientific work. Use the precision field to control the displayed result. Check that radius and axis values are positive. If two line points are identical, choose different points. General form is not just a final answer. It is a reliable bridge between equation styles.

When To Export Results

Exported files save time during repeated practice. A CSV file is ideal for tables. A PDF file is better for sharing. Keep the downloaded record with the original values. This makes later review easier. It also helps you prove which inputs created each final equation. Clear records reduce confusion during tests or projects in class.

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. Conics often use Ax² + Bxy + Cy² + Dx + Ey + F = 0.

Which equation types are supported?

The calculator supports slope intercept lines, point slope lines, two point lines, circles, ellipses, vertical parabolas, horizontal parabolas, and quadratic models. Each type has its own input group.

Can I convert a circle to general form?

Yes. Enter h, k, and radius r from standard circle form. The tool expands both squared terms and moves the radius value to the left side.

Why is radius required to be positive?

A circle radius represents distance from the center. Distance cannot be zero or negative for a valid circle. The calculator warns you when the radius is not valid.

What precision should I use?

Use two to four decimals for most homework. Use more decimals for scientific or engineering work. Use zero decimals when your values are whole numbers and exact rounding is acceptable.

Does the calculator show steps?

Yes. After submission, the answer appears above the form with coefficients and short expansion steps. This helps users understand how the final equation was created.

Can I export my result?

Yes. Use the CSV button for spreadsheet records. Use the PDF button for a simple printable report. Both options become available after a successful calculation.

Why do identical points fail?

Two identical points cannot define a unique line. A line through two points needs two different locations. Enter a different second point to create a valid equation.