Circle Equation Calculator

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

  

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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