Virginia SOL Math / Geometry / Polygons & Circles
Equations of Circles
What you'll learn
- Write the equation of a circle from its center and radius
- Identify the center and radius from an equation
- Graph a circle on the coordinate plane
Words to know
- Standard form —
- (x - h)^2 + (y - k)^2 = r^2 for a circle
- Center —
- the point (h, k) at the middle of the circle
- Radius —
- the distance r from the center to the circle
- Coordinate plane —
- the grid formed by the x-axis and y-axis
Why it matters Circle equations let computers and engineers place and detect round regions, from GPS range rings to collision zones in games.
Worked examples
Model ItI do
Write the equation of the circle with center (3, 3) and radius 2 shown on the grid.
Use (x - h)^2 + (y - k)^2 = r^2 with h = 3, k = 3, r = 2. The equation is (x - 3)^2 + (y - 3)^2 = 4.
Try It TogetherWe do
Find the center and radius of (x + 1)^2 + (y - 5)^2 = 36.
Rewrite x + 1 as x - (-1), so h = -1 and k = 5, giving center (-1, 5). Since r^2 = 36, the radius is sqrt(36) = 6.
Now YouYou do
Write the equation of the circle with center (0, 0) and radius 5.
Substitute h = 0, k = 0, and r = 5 into the standard form. Check your answer in the back of this chapter.
Practice
Mastered 0 of 11
Warm-up
Ease in with the basics.
1.Write the equation of a circle with center (2, 0) and radius 3.
2.Find the center of (x - 4)^2 + (y + 2)^2 = 9.
3.Find the radius of (x - 1)^2 + (y - 1)^2 = 49.
On Level
The core Quick Check from the book.
1.Write the equation of a circle with center (2, 0) and radius 3.
2.Find the center of (x - 4)^2 + (y + 2)^2 = 9.
3.Find the radius of (x - 1)^2 + (y - 1)^2 = 49.
4.What is r^2 for a circle of radius 8?
5.Is (x - 3)^2 + (y - 3)^2 = 4 centered at (3, 3) or (-3, -3)?
Challenge
Stretch your thinking.
1.Write the equation of the circle with center (-3, 5) and radius 4.
2.A circle has center (2, -1) and passes through the point (2, 4). Find its radius.
3.Find the center and radius of (x + 6)^2 + (y - 2)^2 = 64.