Circle Equation Calculator
Convert circle equations between standard, general, and parametric forms.
For equation: x² + y² + Dx + Ey + F = 0
Parametric form uses the same center and radius as standard form.
Circle Properties
Center
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Radius
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Equation Forms
Standard Form
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General Form
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Parametric Form
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Circle Equation Forms
A circle can be represented in three main equation forms, each useful for different purposes.
1. Standard Form
Formula: (x - h)² + (y - k)² = r²
Where (h, k) is the center and r is the radius. This form clearly shows the center and radius, making it ideal for graphing and understanding the circle's position and size.
2. General Form
Formula: x² + y² + Dx + Ey + F = 0
Where:
- D = -2h
- E = -2k
- F = h² + k² - r²
This form is useful for algebraic manipulation and solving systems of equations.
3. Parametric Form
Formulas:
- x = h + r·cos(t)
- y = k + r·sin(t)
Where t is a parameter (typically 0 ≤ t ≤ 2π). This form is useful for tracing the circle point by point and in computer graphics applications.
Converting Between Forms
From General to Standard:
- h = -D/2
- k = -E/2
- r = √(h² + k² - F)
Example: A circle with center (3, -2) and radius 4 has:
• Standard form: (x - 3)² + (y + 2)² = 16
• General form: x² + y² - 6x + 4y - 3 = 0
• Parametric form: x = 3 + 4cos(t), y = -2 + 4sin(t)
This calculator provides mathematical conversions between circle equation forms based on standard formulas. Results are for educational and informational purposes. While we strive for accuracy, please verify important calculations independently.
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