Circle Equation Calculator

Circle Equation using (h,k) and(h,k)=(,) and radius (r) =
Diameter PointsA = (,) and B = (,)
Enter Circle Equation

Find the equation of a circle that has a diameter with the endpoints given by the points A(1,1) and B(2,4)

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 =1 + 4
2

k =5
2

k = 2.5
From above, the center of our circle is (h, k) = (1.5, 2.5)

Calculate radius:
r = Square Root((x2 - x1)2 + (y2 - y1)2)
r = Square Root((2 - 1)2 + (4 - 1)2)
r = ½Square Root((12 + 32))
r = ½√(1 + 9)
r = ½√10
r = ½√10
r = ½(3.4)
r = 1.5811

Now calculate our circle equation using (h, k), and r
Find the equation of the circle with center (h,k) = (1.5,2.5) and radius r = 1.5811
The standard equation for a circle is (x - h)2 + (y - k)2 = r2

Plugging in our numbers, we get:
(x - 1.5)2 + (y - 2.5)2 = 1.58112
(x - 1.5)2 + (y - 2.5)2 = 2.49987721

Determine the general form of the circle equation given center (h, k) = (1.5, 2.5) and radius r = 1.5811:
Expanding the standard form, we get the general form of x2 + y2 - 2hx - 2ky + h2 + k2 - r2 = 0

Plugging in our values for h,k, and r, we get:
Expanding the standard form, we get the general form of x2 + y2 - 2(1.5)x - 2(2.5)y + 1.52 + 2.52 - 1.58112 = 0
x2 + y2 - 3x - 5y + 2.25 + 6.25 - 2.49987721 = 0
Combining our constants, we have our general form of a circle equation below:
x2 + y2 - 3x - 5y + 6.00012279 = 0