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Two Implicit Lines Intersection

Online two implicit lines intersection. Parallel or coincident lines have zero determinant and are rejected.

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two implicit lines intersection calculator online

Use two implicit lines intersection online for a1, b1, c1, a2, b2, c2. Parallel or coincident lines have zero determinant and are rejected. Finite floating-point calculation with the displayed domain; large integer counts can lose exact precision.

How to use it

Enter a1. Set b1, c1, a2, b2, c2. Select Calculate and check the labeled output. Copy or download the JSON result.

Options and example settings

OptionChoices / valueExample default
a1Main input. Signed finite values. 1
b1Option. Signed finite values. 1
c1Option. Signed finite values. -4
a2Option. Signed finite values. 1
b2Option. Signed finite values. -1
c2Option. Signed finite values. 0

Calculation method

x = (b1*c2-b2*c1)/(a1*b2-a2*b1); y = (c1*a2-c2*a1)/(a1*b2-a2*b1) (^ means exponentiation; trig functions ending in d use degrees).

Worked examples

Apply two implicit lines intersection to the case below, keeping the displayed units and assumptions. Parallel or coincident lines have zero determinant and are rejected.

Two Implicit Lines Intersection — worked case

Settings: b1: 1; c1: -4; a2: 1; b2: -1; c2: 0

Input:

1

Calculated result for these inputs:

Output:

{
  "x": 2,
  "y": 2
}

Choose the right tool

Choose number theory for exact integer relationships, distribution tools for a declared random model, and geometry tools for coordinates. A density is not a probability and a statistical model does not establish a real-world outcome.

Limitations and common mistakes

  • Parallel or coincident lines have zero determinant and are rejected. Finite floating-point calculation with the displayed domain; large integer counts can lose exact precision.
  • Use the displayed unit in every field. Ratios and percentages are different inputs; percent fields use values such as 25 rather than 0.25.

Frequently asked questions

How can I use two implicit lines intersection calculator online?

Enter a1. Set b1, c1, a2, b2, c2. Select Calculate and check the labeled output. Copy or download the JSON result.

Where is my input processed?

The bundled tool processes input in your browser. It does not upload tool input to a conversion service. Other site plugins, analytics, advertising and browser extensions may have separate behavior.

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