Find the equation of a circle with
Diameter endpoints = A(1,1) and B(2,4)
Step 1: Find the Midpoint (
h ,
k ) of
AB :
h =
1.5 k =
2.5 Center of our circle is (
h ,
k ) = (
1.5 ,
2.5 )
Calculate radius: r = Square Root((x
2 - x
1 )
2 + (y
2 - y
1 )
2 )
r = Square Root((2 - 1)
2 + (4 - 1)
2 )
r = ½Square Root((1
2 + 3
2 ))
r = ½√
(1 + 9) r = ½√
10 r = ½(3.1622776601684)
r = 1.5811
Find circle equation Find the equation of the circle with
center (
h ,
k ) = (
1.5 ,
2.5 ) and radius
r =
1.5811 Standard Circle Equation: (x -
h )
2 + (y -
k )
2 =
r 2 Plugging in our numbers, we get: (x -
1.5 )
2 + (y -
2.5 )
2 =
1.5811 2 (x - 1.5)2 + (y - 2.5)2 = 2.49987721 General form of circle equation Center (
h ,
k ) = (
1.5 ,
2.5 ) and r =
r =
1.5811 :
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(
2.5 )y +
1.5 2 +
2.5 2 -
1.5811 2 = 0
x
2 + y
2 - 3x - 5y + 2.25 + 6.25 - 2.49987721 = 0
Combine our constants x2 + y2 - 3x - 5y + 6.00012279 = 0 x2 + y2 - 3x - 5y + 6.00012279 = 0
You have 2 free calculationss remaining
What is the Answer?
x2 + y2 - 3x - 5y + 6.00012279 = 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 = 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
Example calculations for the Circle Equation Calculator Circle Equation Calculator Video VIDEO
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