Circle from Center and Radius
Circle from Center and Radius
\[\begin{aligned}
y &= k+\sqrt{r^2-(x-h)^2} \\
y &= k-\sqrt{r^2-(x-h)^2}
\end{aligned}\]
Variables
x = x-coordinate
y1 = upper y-coordinate
y2 = lower y-coordinate
h = x-coordinate of center
k = y-coordinate of center
r = radius
Description
What is this formula?
This formula defines a circle using its center coordinates and radius. The explicit form calculates the upper and lower y-values for a given x-coordinate.
When to use it
Use this formula when graphing a circle or calculating points located on a circle from its center and radius.
Example
For a circle centered at (1,2) with radius 5:
y = 2 ± √(25 - (x-1)^2)
Applications
- Analytic geometry
- Coordinate graphing
- CAD and computer graphics
- Engineering design
- Mathematical modeling
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