SAT Circle Equations Made Easy with Desmos
SAT circle questions often hide the center and radius inside an expanded equation. Desmos graphs it instantly so you can read the geometry off the screen.
Step by step
- 1
Type the equation exactly as given
Desmos graphs implicit equations, so paste the circle as-is — standard form (x − 3)² + (y + 4)² = 25 OR expanded form x² + y² − 6x + 8y = 0. No completing the square needed.
- 2
Let Desmos draw the circle
The full circle appears on screen immediately.
- 3
Find the center
The center sits in the middle. Click the far-left and far-right points — the center's x is halfway between them; the top and bottom points give the center's y.
- 4
Find the radius
The radius is the distance from the center to any edge — for example, half the horizontal width: (rightmost x − leftmost x) ÷ 2.
- 5
Answer the question
Center, radius, or whether a point is inside / on the circle — all readable straight off the graph.
Pro tip
If the equation is already in standard form (x − h)² + (y − k)² = r², read the center (h, k) and radius r directly — but watch signs: (x − 3)² means h = +3, and (y + 4)² means k = −4.
Try it yourself
Work the example right here in a live Desmos calculator — no Bluebook needed.
x² + y² − 6x + 8y = 0. What is the radius of the circle?
Graph the circle, then click its leftmost and rightmost points to find the center and radius.
Loading interactive calculator…
Show the answer
Answer: 5
Graph the equation as-is. The circle's leftmost point is (−2, −4) and rightmost is (8, −4), so the diameter is 10 and the radius is 5. (Algebra check: complete the square → (x − 3)² + (y + 4)² = 25, so r = 5.)
Put the trick to work on a real test
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