Circle Equation Calculator

Circle Equation Calculator Image to Crop

Find the equation of a circle with
Diameter endpoints = A(11,18) and B(-13,-19)

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

h =	A1 + B1
	2

h =	11 + -13
	2

h =	-2
	2

h = -1

k =	A2 + B2
	2

k =	18 + -19
	2

k =	-1
	2

k = -0.5
Center of our circle is (h, k) = (-1, -0.5)

Calculate radius:

r = Square Root((x2 - x1)2 + (y2 - y1)2)
r = Square Root((-13 - 11)2 + (-19 - 18)2)
r = ½Square Root((-242 + -372))
r = ½√(576 + 1369)
r = ½√1945
r = ½(44.1021541424)
r = 22.0511

Find circle equation

Find the equation of the circle with
center (h,k) = (-1,-0.5) and radius r = 22.0511

Standard Circle Equation:

(x - h)2 + (y - k)2 = r2

Plugging in our numbers, we get:

(x - (-1))2 + (y - (-0.5))2 = 22.05112
(x + 1)2 + (y + 0.5)2 = 486.25101121

General form of circle equation

Center (h, k) = (-1, -0.5) and r = r = 22.0511:

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)x - 2(-0.5)y + -12 + -0.52 - 22.05112 = 0
x2 + y2 + 2x + y + 1 + 0.25 - 486.25101121 = 0

Combine our constants

x2 + y2 + 2x + y - 485.00101121 = 0

You have 1 free calculations remaining

What is the Answer?

x2 + y2 + 2x + y - 485.00101121 = 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 = r2 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?

centercirclethe set of all points in the plane that are a fixed distance from a fixed pointcircle equationAn equation used to graph a circlediameterdistance from two endpoints of a circle through the center
d = 2requationa statement declaring two mathematical expressions are equalmidpointthe middle point of a line segment. It is equidistant from both endpoints. It bisects the segment.originOn a two digit coordinate plane, the point (0, 0), where the x-axis and y-axis cross.radiusDistance from the center of a circle to the edge
C/2π

Example calculations for the Circle Equation Calculator