Graph a Circle from Its Equation
The equation (x − h)² + (y − k)² = r² graphs a circle with center (h, k) and radius r; x² + y² = 16 is a circle of radius 4 centered at the origin.
At a glance
| What it is | Graph circles online from their equation. x² + y² = r² is centered at the origin; (x − h)² + (y − k)² = r² is centered at (h, k). Free. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| Center at origin | x² + y² = r² |
|---|---|
| General center | (x − h)² + (y − k)² = r², center (h, k) |
| Radius | r = √(right-hand side) |
| Example | (x − 2)² + (y − 1)² = 4: center (2, 1), radius 2 |
How do you graph an equation that is not a function?
A circle fails the vertical line test, so it cannot be written as y = f(x). Plotline graphs any equation in x and y directly, so you can type the circle exactly as it is written.
How to use it in Plotline
- The graph of x² + y² = 16 and (x − 2)² + (y − 1)² = 4 is already loaded above. Edit the equation in the list to change it.
- Drag the graph to move around, scroll or pinch to zoom, and tap the crosshair to reset the view.
- Hover over or tap the curve to read the coordinates of any point.
- Press Enter to add another equation and compare graphs in different colors.
Frequently asked questions
How do I find the radius from the equation?
Compare the equation with (x − h)² + (y − k)² = r². The number on the right is r², so take its square root: in x² + y² = 16, r² = 16 and the radius is 4, centred on the origin.
Is it free?
Yes. The graphing calculator is free with no account and no sign-up: plot as many equations as you like, use sliders, save graphs in your browser and share them by link. It installs as an app and keeps working offline.
Learn more
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Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.