Standard equation of circle


General equation of circle


Parametric equations of a circle


# Equation of a Circle Calculator

Writing an equation of a circle using different parameters like coordinates, radius, and others can spin your head. Doesn’t matter how much proficiency you have in Geometry, you will still find complications. But you can get it done through a simple approach using the Equation of a circle calculator.

Using this online Maths calculator, you can get the equation of a circle in all its three major types. It means that this calculator will show you the standard, general, and parametric equations of a circle using your given input. So, you won’t have to worry whether you need a general equation or a parametric equation for practical mathematics. Want to learn about it more? Keep reading!

## What is the equation of a circle?

To learn about the equation of a circle and its different types, you need to understand what is a circle first. A circle is a geometrical two-dimensional round figure on the surface of which all points have the same distance from a fixed point called the center of a circle.

The equation of a circle is a specific algebraic expression that shows whether the given points can be part of the circumference of a circle or not. If a point fulfills the equation of a circle, it means that the point will be located on the circumference.

Depending on the type of coordinates given, an equation of a circle can be written in three different types. These types are described briefly here in the following section.

### Standard Equation of a Circle

It is the basic equation of the circle that describes the points located on the circumference of the circle. Here is how to write the standard equation of a circle.

(x - A)2 + (y - B)2 = r2


Here, A & B are the coordinates of the center of a circle while “r” is the radius of that circle.

## General Equation of a circle

Another type of equation of a circle is the general type. It is not used mostly because it is a complicated process to get information from this equation. But you can easily convert a general equation of motion to its standard form. Here is how you can write the general equation of a circle.

x2 + ax + y2 + by + c = 0


In this equation, “a”, “b”, and “ c” are three different coefficients that will depend on the coordinates of the circle.

## Parametric Equation of a circle

The third and last type of equation of a circle is called the parametric equation because of its dependence on the angle of that circle. As the word parameter refers to theta that is used to represent the measurement of an angle, that’s why it is called a parametric equation of a circle/ Here is how we can write this equation of a circle.

x = rcosθ + x0

y = rsinθ + y0


In the above equations, “r” refers to the radius of the circle while “x0” and “y0” are the coordinates of the circle. Similarly, “θ” refers to the angle of the circle.

## Equation of a circle formula

Till now, you have got an idea about the equation of a circle and its types. Let us now share a formula using which you can write a standard equation of a circle.

(x - A)2 + (y - B)2 = r2


You only have to put the coordinates of the center of the circle and solve the above basic Mathematical operations. In the end, you will get a resultant equation that we call an equation of a circle.

### How to find the equation of a circle?

To let you understand how to calculate the equation of a circle, we have solved an example here. The following example shows how to write and solve a standard equation of a circle using the given coordinates.

Example 1:

Write an equation of a circle when the coordinates of the center of that circle are (2, 7) and the radius is 6.

Solution:

As we know,

(x - A)2 + (y - B)2 = r2


Also, we have been given the values of r, A, and B. So, we have to put those values in the above equation.

(x - 2)2 + (y - 7)2 = (6)2

x2 -4x +4 + y2 -14y +49 = 36


By solving the above equation, we have found the final output.

x2 -4x + y2 -14y +17 = 0


### How to use the equation of a circle calculator?

If you are facing complications in writing an equation of a circle, you should use this tool by Calculator’s Bag. This calculator will not only show you the standard form of the equation but also the final output when the equation will be converted to other types. Here are the steps you need to follow for using this tool.

• Insert the “x” and “y” coordinates of the center of the circle
• Put the value of the radius
• This calculator will automatically show the standard form of the equation of that circle

### FAQ | Equation of a Circle Calculator

What is the equation for a circle in the standard form calculator?

In the standard form, an equation of a circle will be written as:

(x - A)2 + (y - B)2 = r2


What is the practical application of the equation of a circle in real life?

These equations are normally used to design round tracks for sports, round building blocks, and Ferris wheels.

Why is the circle theorem important?

Circle theorems are important because we can easily find the missing values of a circle including angles without using multiple tools.

What is the purpose of the equation of a circle?

The equation of a circle defines the entire properties of a circle including the points feasibility on its circumference.

How do you find the missing angle of a circle?

Using the parametric equation of a circle, we can find the missing angles of a circle. We can also use a protector to do this practice if we don’t want to solve the equation.