Find the equation of a circle with

Diameter endpoints = A(1,4) and B(2,6)

Step 1: Find the Midpoint (

h ,

k ) of

AB :

h =

1.5 k =

5 Center of our circle is (

h ,

k ) = (

1.5 ,

5 )

Calculate radius: r = Square Root((x

_{2} - x

_{1} )

^{2} + (y

_{2} - y

_{1} )

^{2} )

r = Square Root((2 - 1)

^{2} + (6 - 4)

^{2} )

r = ½Square Root((1

^{2} + 2

^{2} ))

r = ½√

(1 + 4) r = ½√

5 r = ½(2.2360679774998)

r = 1.118

Find circle equation Find the equation of the circle with

center (

h ,

k ) = (

1.5 ,

5 ) and radius

r =

1.118 Standard Circle Equation: (x -

h )

^{2} + (y -

k )

^{2} =

r ^{2} Plugging in our numbers, we get: (x -

1.5 )

^{2} + (y -

5 )

^{2} =

1.118 ^{2} (x - 1.5)^{2} + (y - 5)^{2} = 1.249924 General form of circle equation Center (

h ,

k ) = (

1.5 ,

5 ) and r =

r =

1.118 :

Expand the standard form x

^{2} + y

^{2} - 2

h x - 2

k y +

h ^{2} +

k ^{2} -

r ^{2} = 0

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

^{2} + y

^{2} - 2(

1.5 )x - 2(

5 )y +

1.5 ^{2} +

5 ^{2} -

1.118 ^{2} = 0

x

^{2} + y

^{2} - 3x - 10y + 2.25 + 25 - 1.249924 = 0

Combine our constants x^{2} + y^{2} - 3x - 10y + 26.000076 = 0 See Answer x^{2} + y^{2} - 3x - 10y + 26.000076 = 0

What is the Answer?
x^{2} + y^{2} - 3x - 10y + 26.000076 = 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(a_{1} ,a_{2} ) and B(b_{1} ,b_{2} )
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} = r

^{2} 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
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