General Form of the Equation of a Circle Calculator
Table of contents
What is the equation of a circle in general form?How do I convert the general equation of a circle to the standard form?How do I convert the general equation of a circle to the parametric form?How do I use the general form of the equation of a circle calculator?Related calculatorsFAQsWelcome to the general form of the equation of a circle calculator, which can help you convert your circle equation from the general form to the standard and parametric forms, or the other way. Here, we'll learn:
- What the equation of a circle in general form looks like;
- How to write the equation of a circle in general form; and
- How to convert the general form of the circle equation to other forms.
What is the equation of a circle in general form?
The general form of the equation of a circle is given as x² + y² + Dx + Ey + F = 0, with the parameters D, E, and F determining the circle's properties such as radius and center.
How do I convert the general equation of a circle to the standard form?
The standard form of the equation of a circle is (x−A)² + (y−B)² = C. We can write the general form of the circle equation to the standard form by calculating the unknowns A, B, and C from the general equation's parameters D, E, and F.
Luckily, that math is easy!
- A = −D/2;
- B = −E/2; and
- C = A² + B² − F.
How do I convert the general equation of a circle to the parametric form?
The parametric form of the equation of a circle is x = A + r cos(α) and y = B + r sin(α). To write the general form of the circle equation to the parametric equation, we calculate the unknowns A, B, and r:
- A = −D/2;
- B = −E/2; and
- r = √(A² + B² − F).
How do I use the general form of the equation of a circle calculator?
The general form of the equation of a circle calculator is easy to use! Here's how:
- Enter your circle's equation in the general form at the top of the calculator.
- Find your circle rewritten in standard and parametric forms below.
- Also find your circle's properties like center, radius, and area at the very bottom.
What is the general form of the equation (x−3)² + (y+2)² = 25?
The general form is x² + y² − 6x + 4y − 12 = 0. Converting from the standard form of (x − A)² + (y − B)² = C (with parameters A = 3, B = −2, and C = 25) to x² + y² + Dx + Ey + F = 0, we calculate:
- D = −2A = −6;
- E = −2B = 4; and
- F = A² + B² − C = −12.
What is the general equation of a circle with (x−6)² + (y−6)² = 49?
This circle's general form is x² + y² − 12x − 12y + 23 = 0. We have A = 6, B = 6, and C = 49 in the standard form (x−A)² + (y−B)² = C. So, to convert to x² + y² + Dx + Ey + F = 0, we calculate:
- D = −2A = −12;
- E = −2B = −12; and
- F = A² + B² − C = 23.
What is the general form of the equation of a circle with (x+3)² + (y−5)² = 49?
The general form is x² + y² + 6x − 10y − 15 = 0. Converting from the standard form of (x−A)² + (y−B)² = C (with parameters A = −3, B = 5, and C = 49) to x² + y² + Dx + Ey + F = 0, we calculate:
- D = −2A = 6;
- E = −2B = −10; and
- F = A² + B² − C = −15.