# Equation of Circle Calculator

What is a 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 among the central point to any set of points on perimeter/circumference is known as the circle's radius.## Equation of a Circle Calculator

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

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

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

x^{2}+ y^{2}+ 2gx + 2fy + c = 0

But in 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' be 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.

Where,

a = the radius

x,y = the points or coordinates of a circle

### Equation of a Circle when the origin is not center

Suppose C(h, k) be 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 distance formula,

(x-h)^{2}+ (y-k)^{2}= CP^{2}

Let radius= CP = a.

So we can write the Equation of a Circle when the origin is not center as;

(x-h)^{2}+ (y-k)^{2}= a^{2}

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

### Example

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.

#### Solution

Given data

Centre = (0, 0)

Radius = 8 units.

To find

Equation of a circle=?

### Formula

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

x^{2}+ y^{2}= a^{2}

Putting the value of radius

x^{2}+ y^{2}= 82

Equation of a circle is

x^{2}+ y^{2}= 64

### 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.