Circle Equation Calculator

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(2,6)

Step 1: Find the Midpoint (h,k) of AB:

h  =	A1 + B1
	2

h  =	1 + 2
	2

h  =	3
	2

h = 1.5

k  =	A2 + B2
	2

k  =	4 + 6
	2

k  =	10
	2

k = 5
Center of our circle is (h, k) = (1.5, 5)

Calculate radius:

r = Square Root((x₂ - x₁)² + (y₂ - y₁)²)
r = Square Root((2 - 1)² + (6 - 4)²)
r = ½Square Root((1² + 2²))
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 = r²

Plugging in our numbers, we get:

(x - 1.5)² + (y - 5)² = 1.118²
(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

x² + y² - 2hx - 2ky + h² + k² - r² = 0

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

x² + y² - 2(1.5)x - 2(5)y + 1.5² + 5² - 1.118² = 0
x² + y² - 3x - 10y + 2.25 + 25 - 1.249924 = 0

Combine our constants

x² + y² - 3x - 10y + 26.000076 = 0