Find the equation of a circle with
Diameter endpoints = A(-1,3) and B(5,9)
Step 1: Find the Midpoint (
h ,
k ) of
AB :
h =
2 k =
6 Center of our circle is (
h ,
k ) = (
2 ,
6 )
Calculate radius: r = Square Root((x
2 - x
1 )
2 + (y
2 - y
1 )
2 )
r = Square Root((5 - -1)
2 + (9 - 3)
2 )
r = ½Square Root((6
2 + 6
2 ))
r = ½√
(36 + 36) r = ½√
72 r = ½(8.4852813742386)
r = 4.2426
Find circle equation Find the equation of the circle with
center (
h ,
k ) = (
2 ,
6 ) and radius
r =
4.2426 Standard Circle Equation: (x -
h )
2 + (y -
k )
2 =
r 2 Plugging in our numbers, we get: (x -
2 )
2 + (y -
6 )
2 =
4.2426 2 (x - 2)2 + (y - 6)2 = 17.99965476 General form of circle equation Center (
h ,
k ) = (
2 ,
6 ) and r =
r =
4.2426 :
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(
2 )x - 2(
6 )y +
2 2 +
6 2 -
4.2426 2 = 0
x
2 + y
2 - 4x - 12y + 4 + 36 - 17.99965476 = 0
Combine our constants x2 + y2 - 4x - 12y + 22.00034524 = 0 x2 + y2 - 4x - 12y + 22.00034524 = 0
Common Core State Standards In This Lesson
What is the Answer?
x2 + y2 - 4x - 12y + 22.00034524 = 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
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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
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