Circle from Diameter Endpoints
Circle from Diameter Endpoints
\[\begin{aligned}
y &= \frac{y_1+y_2}{2}+\sqrt{\left(\frac{(x_2-x_1)^2+(y_2-y_1)^2}{4}\right)-\left(x-\frac{x_1+x_2}{2}\right)^2} \\
y &= \frac{y_1+y_2}{2}-\sqrt{\left(\frac{(x_2-x_1)^2+(y_2-y_1)^2}{4}\right)-\left(x-\frac{x_1+x_2}{2}\right)^2}
\end{aligned}\]
Variables
x = x-coordinate
y1 = upper y-coordinate
y2 = lower y-coordinate
x1p = x-coordinate of first endpoint
y1p = y-coordinate of first endpoint
x2p = x-coordinate of second endpoint
y2p = y-coordinate of second endpoint
Description
What is this formula?
This formula defines a circle using the endpoints of its diameter. The center is calculated as the midpoint of the diameter, and the radius is half the distance between the endpoints.
When to use it
Use this formula when the endpoints of a circle diameter are known and the explicit circle equation is needed.
Example
For diameter endpoints at (-2,0) and (2,0):
y = 0 ± √(4 - x²)
Applications
- Analytic geometry
- Coordinate calculations
- CAD and graphics
- Engineering design
- Mathematical modeling
Download the fCalc app to calculate this formula and thousands more:
