 # Circle Equation Calculator

 Radius and Center(h,k)=(,)and r = Diameter PointsA = (,)B = (,) Circle Equation

Find the equation of a circle with
Diameter endpoints = A(1,4) and B(5,6)

Step 1: Find the Midpoint (h,k) of AB:
 h  = A1 + B1 2

 h  = 1 + 5 2

 h  = 6 2

h = 3

 k  = A2 + B2 2

 k  = 4 + 6 2

 k  = 10 2

k = 5
Center of our circle is (h, k) = (3, 5)

r = Square Root((x2 - x1)2 + (y2 - y1)2)
r = Square Root((5 - 1)2 + (6 - 4)2)
r = ½Square Root((42 + 22))
r = ½√(16 + 4)
r = ½√20
r = ½(4.4721359549996)
r = 2.2361

## Find circle equation

Find the equation of the circle with
center (h,k) = (3,5) and radius r = 2.2361

## Standard Circle Equation:

(x - h)2 + (y - k)2 = r2

## Plugging in our numbers, we get:

(x - 3)2 + (y - 5)2 = 2.23612
(x - 3)2 + (y - 5)2 = 5.00014321

## General form of circle equation

Center (h, k) = (3, 5) and r = r = 2.2361:

## Expand the standard form

x2 + y2 - 2hx - 2ky + h2 + k2 - r2 = 0

## Plugg in our values for h,k, and r:

x2 + y2 - 2(3)x - 2(5)y + 32 + 52 - 2.23612 = 0
x2 + y2 - 6x - 10y + 9 + 25 - 5.00014321 = 0

## Combine our constants

x2 + y2 - 6x - 10y + 28.99985679 = 0

x2 + y2 - 6x - 10y + 28.99985679 = 0

### How does the Circle Equation Calculator work?

Free Circle Equation Calculator - This calculates the standard equation of a circle and general equation of a circle from the following given items:
* A center (h,k) and a radius r
* A diameter A(a1,a2) and B(b1,b2)
This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.
This calculator has 8 inputs.

### What 1 formula is used for the Circle Equation Calculator?

1. (x - h)2 + (y - k)2 = r2 where (h,k) is the center of the circle and r = radius.

For more math formulas, check out our Formula Dossier

### What 8 concepts are covered in the Circle Equation Calculator?

center
circle
the set of all points in the plane that are a fixed distance from a fixed point
circle equation
An equation used to graph a circle
diameter
distance from two endpoints of a circle through the center
d = 2r
equation
a statement declaring two mathematical expressions are equal
midpoint
the middle point of a line segment. It is equidistant from both endpoints. It bisects the segment.
origin
On a two digit coordinate plane, the point (0, 0), where the x-axis and y-axis cross.