# 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.