Circle Equation Calculator

Publish date: 2024-06-29

Circle Equation Calculator Image to Crop

Find the equation of a circle with
Diameter endpoints = A(-4,5) and B(7,-3)

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

h =	A1 + B1
	2

h =	-4 + 7
	2

h =	3
	2

h = 1.5

k =	A2 + B2
	2

k =	5 + -3
	2

k =	2
	2

k = 1
Center of our circle is (h, k) = (1.5, 1)

Calculate radius:

r = Square Root((x2 - x1)2 + (y2 - y1)2)
r = Square Root((7 - -4)2 + (-3 - 5)2)
r = ½Square Root((112 + -82))
r = ½√(121 + 64)
r = ½√185
r = ½(13.601470508735)
r = 6.8007

Find circle equation

Find the equation of the circle with
center (h,k) = (1.5,1) and radius r = 6.8007

Standard Circle Equation:

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

Plugging in our numbers, we get:

(x - 1.5)2 + (y - 1)2 = 6.80072
(x - 1.5)2 + (y - 1)2 = 46.24952049

General form of circle equation

Center (h, k) = (1.5, 1) and r = r = 6.8007:

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(1)y + 1.52 + 12 - 6.80072 = 0
x2 + y2 - 3x - 2y + 2.25 + 1 - 46.24952049 = 0

Combine our constants

x2 + y2 - 3x - 2y - 42.99952049 = 0

You have 1 free calculations remaining

What is the Answer?

x2 + y2 - 3x - 2y - 42.99952049 = 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