Standard equation of circle
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General equation of circle
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Parametric equations of a circle
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​Equation of Circle

A circle is a set of points separated equally from its origin. Whereas the origin is a central point of a circle, also known as the center of a circle. The interval between the central point to any set of points on the perimeter/circumference is known as the circle's radius.

When an arc is drawn from the center's fixed point, all the curve points have an equal interval from the central point. Some of you may raise the question that the circle is functions or not. The answer is no. Because every value represents an average value of a function in the domain that is precisely linked with an individual point in the respective area, but a line that crosses through the circle intersects the line at two points on the outside.


Explanation of ​Equation of Circle Calculator

To understand circle is an equation, let's have some mathematical descriptions here.

The general form of the circle's equation is listed below:

x2 + y2 + 2gx + 2fy + c = 0

But in the two scenarios, the equation of a circle is different.

  • When the Origin is Center

  • When the origin is not center

  • Equation of a Circle when an origin is in the center

Suppose an absolute point P(x, y), and 'a' is the circle's radius equivalent to OP.

The interval among the point (x, y) and origin (0,0)can be determined by utilizing the distance formula.

Now by applying a square on both sides, we will get the equation of a Circle when an origin is in the center.


a = the radius
x,y = the points or coordinates of a circle


Visit our Circle Calculator to know more about the circle.

Equation of a Circle when the origin is not center

Suppose C(h, k) is the circle's center and P(x, y) is any circle's point.

So the radius of a circle can be narrated as CP. By applying the distance formula,

(x-h)2 + (y-k)2 = CP2


radius = CP = a

So we can write the Equation of a Circle when the origin is not centered as:

(x-h)2 + (y-k)2 = a2

This equation is also known as the circle's standard form for equation. Also known as the circle's standard form for the equation.


To clarify your concepts, completely let's have an example below:

Suppose a circle whose origin is in the center and has 8 units of the radius, find the circle equation.

Given data

Centre = (0, 0)
Radius = 8 units.

To Find

Equation of a circle = ?

Formula of ​Equation of Circle Calculator

We know the Equation of a Circle when an origin is in the center

x2 + y2 = a2

Putting the value of the radius

x2 + y2 = 82

The equation of a circle is

x2 + y2 = 64

How to use ​Equation of Circle Calculator?

The steps to use ​the equation of a circle calculator are as follows:

Step 1: Enter the value of x in the first required input.

Step 2: Enter the value of y in the second required input.

Step 3: Enter the value of r in the third required input.

Step 4: The calculator will automatically display an answer on the screen.

Calculator use

To immediately get the circle's equation, you can use the equation of a circle calculator by putting the values in it; the resultant answer will appear on the screen. This Calculator will deliver the prescribed solution to your questions. To resolve complicated problems, this Calculator is programmed for you.