Radius and Center
(h,k)=(,)
and r =
Diameter Points
A = (,)
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)

Calculate radius:

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





What is the Answer?
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?

(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.
radius
Distance from the center of a circle to the edge
C/2π
Example calculations for the Circle Equation Calculator
Circle Equation Calculator Video

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