Equation of a Circle from Diameter Endpoints
Find the equation of a circle given the endpoints of its diameter. Enter two points (x1,y1) and (x2,y2) to get the center, radius, and standard form equation (x-h)^2+(y-k)^2=r^2.
Enter the endpoints of the diameter (x₁, y₁) and (x₂, y₂):
About This Calculator
This calculator finds the equation of a circle when the endpoints of its diameter are known. Given two points (x1,y1) and (x2,y2) that form the diameter, the center (h,k) is the midpoint: h = (x1 + x2)/2, k = (y1 + y2)/2. The radius r is half the distance between the endpoints: r = 1/2sqrt((x2-x1)^2 + (y2-y1)^2).
The resulting standard equation is displayed as (x-h)^2 + (y-k)^2 = r^2. This is a fundamental topic in coordinate geometry taught across high school curricula in India (CBSE Class 11), US (Common Core Geometry), and UK (A-Level Mathematics).
Frequently Asked Questions
How do you find the equation of a circle from diameter endpoints?
Given endpoints (x1,y1) and (x2,y2) of a diameter: the center is the midpoint ((x1+x2)/2, (y1+y2)/2), and the radius is half the distance between the endpoints. The standard equation is (x-h)^2 + (y-k)^2 = r^2.
What is the standard form of a circle equation?
The standard form of a circle equation is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius. Any point (x,y) on the circle satisfies this relationship -- its distance to the center equals exactly r.
Is this calculator free?
Yes, all calculators on Calculy are completely free to use.